Find the best tutors and institutes for Class 12 Tuition
Search in
Find the general solution of the differential equation:
The given differential equation is:
Now, integrating both sides, we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Now, integrating both sides of this equation, we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Now, integrating both sides of this equation, we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Integrating both sides of this equation, we get:
Substituting these values in equation (1), we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Integrating both sides of this equation, we get:
Let (ex + e–x) = t.
Differentiating both sides with respect to x, we get:
Substituting this value in equation (1), we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Integrating both sides of this equation, we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Integrating both sides, we get:
Substituting this value in equation (1), we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Integrating both sides, we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Integrating both sides, we get:
Substituting this value in equation (1), we get:
This is the required general solution of the given differential equation.
Find the general solution of the differential equation:
The given differential equation is:
Integrating both sides, we get:
Substituting the values of 
in equation (1), we get:
This is the required general solution of the given differential equation.
For the given differential equation, find a particular solution satisfying the given condition:
just integrate it ...dy=dx/cosa
than a@ x=a and y=1 find the solution
which is y=x/cosa+1
For the given differential equation, find a particular solution satisfying the given condition:
Integrating both sides, we get:
Substituting C = 1 in equation (1), we get:
y = sec x
For the differential equation 
find the solution curve passing through the point (1, –1).
The differential equation of the given curve is:
Integrating both sides, we get:
Now, the curve passes through point (1, –1).
Substituting C = –2 in equation (1), we get:
This is the required solution of the given curve.
Find the general solution of the differential equation:
Sin-1(y/2)=2x+c
For the given differential equation, find a particular solution satisfying the given condition:
The given differential equation is:
Integrating both sides, we get:
Comparing the coefficients of x2 and x, we get:
A + B = 2
B + C = 1
A + C = 0
Solving these equations, we get:
Substituting the values of A, B, and C in equation (2), we get:
Therefore, equation (1) becomes:
Substituting C = 1 in equation (3), we get:
For the given differential equation, find a particular solution satisfying the given condition:
Integrating both sides, we get:
Comparing the coefficients of x2, x, and constant, we get:
Solving these equations, we get 
Substituting the values of A, B, and C in equation (2), we get:
Therefore, equation (1) becomes:
Substituting the value of k2 in equation (3), we get:
For the given differential equation, find a particular solution satisfying the given condition:
Integrating both sides, we get:
Substituting C = 1 in equation (1), we get:
For the given differential equation, find a particular solution satisfying the given condition:
Integrating both sides, we get:
Substituting C = 1 in equation (1), we get:
y = sec x
Find the equation of a curve passing through the point (0, 0) and whose differential equation is
.
The differential equation of the curve is:
Integrating both sides, we get:
Substituting this value in equation (1), we get:
Now, the curve passes through point (0, 0).
Substituting 
in equation (2), we get:
Hence, the required equation of the curve is
For the differential equation find the solution curve passing through the point (1, –1).
The differential equation of the given curve is:
Integrating both sides, we get:
Now, the curve passes through point (1, –1).
Substituting C = –2 in equation (1), we get:
This is the required solution of the given curve.
Find the equation of a curve passing through the point (0, –2) given that at any point 
on the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.
Let x and y be the x-coordinate and y-coordinate of the curve respectively.
We know that the slope of a tangent to the curve in the coordinate axis is given by the relation,
According to the given information, we get:
Integrating both sides, we get:
Now, the curve passes through point (0, –2).
∴ (–2)2 – 02 = 2C
⇒ 2C = 4
Substituting 2C = 4 in equation (1), we get:
y2 – x2 = 4
This is the required equation of the curve.
At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (–4, –3). Find the equation of the curve given that it passes through (–2, 1).
It is given that (x, y) is the point of contact of the curve and its tangent.
The slope (m1) of the line segment joining (x, y) and (–4, –3) is 
We know that the slope of the tangent to the curve is given by the relation,
According to the given information:
Integrating both sides, we get:
This is the general equation of the curve.
It is given that it passes through point (–2, 1).
Substituting C = 1 in equation (1), we get:
y + 3 = (x + 4)2
This is the required equation of the curve.
The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.
Let the rate of change of the volume of the balloon be k (where k is a constant).
Integrating both sides, we get:
⇒ 4π × 33 = 3 (k × 0 + C)
⇒ 108π = 3C
⇒ C = 36π
At t = 3, r = 6:
⇒ 4π × 63 = 3 (k × 3 + C)
⇒ 864π = 3 (3k + 36π)
⇒ 3k = –288π – 36π = 252π
⇒ k = 84π
Substituting the values of k and C in equation (1), we get:
Thus, the radius of the balloon after t seconds is
.
In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years
.
Let p and t be the principal and time respectively.
It is given that the principal increases continuously at the rate of 5% per year.
Integrating both sides, we get:
Now, when t = 0, p = 1000.
⇒ 1000 = eC … (2)
At t = 10, equation (1) becomes:
Hence, after 10 years the amount will worth Rs 1648.
In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?
Let y be the number of bacteria at any instant t.
It is given that the rate of growth of the bacteria is proportional to the number present.
Integrating both sides, we get:
Let y0 be the number of bacteria at t = 0.
⇒ log y0 = C
Substituting the value of C in equation (1), we get:
Also, it is given that the number of bacteria increases by 10% in 2 hours.
Substituting this value in equation (2), we get:
Therefore, equation (2) becomes:
Now, let the time when the number of bacteria increases from 100000 to 200000 be t1.
⇒ y = 2y0 at t = t1
From equation (4), we get:
Hence, in 
hours the number of bacteria increases from 100000 to 200000.
The general solution of the differential equation 
A. 
B. 
C. 
D. 
Integrating both sides, we get:
Hence, the correct answer is A.
How helpful was it?
How can we Improve it?
Please tell us how it changed your life *
Please enter your feedback
UrbanPro.com helps you to connect with the best Class 12 Tuition in India. Post Your Requirement today and get connected.
Find best tutors for Class 12 Tuition Classes by posting a requirement.
Get started now, by booking a Free Demo Class
