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Lesson Posted on 17 Aug Differential Equations

Basics of Differntial equation

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

Differential equation are those equation which contain dependent ,independent variables,derivaives and partial derivatives order: the order of the differential equation is the order of the derivative of the highest order occurring in the differential equation. Degree: The degree of a differential... read more

Differential equation

are those equation which contain dependent ,independent variables,derivaives and partial derivatives

 

order:

the order of the differential equation is the order of the derivative

of the highest order occurring in the differential equation.

 

Degree:

The degree of a differential equation is the degree of the highest order differential coefficient appearing in it subject to the condition, that it can be expressed as a polynomial equation in derivatives.

 

General solution:

A solution in which the number of constants is equal to the order of

the equation is called the general solution of a differential

equation.

Particular Solution:

Particular solutions are derived from the general solution by assigning different values to the constants of a general solution.

 

 

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Lesson Posted on 27/12/2017 Differential Equations

Ordinary & Partial Differential Equation

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

Ordinary Differential Equation: One depedent variable(Y) is dependent only on one independent variable(X). Y is completely dependent on X. Generally, Wife(Y) is completely dependent on Husband(X). An ordinary differential equation (ODE) has only derivatives of one variable that is, it has no partial... read more

Ordinary Differential Equation:

One depedent variable(Y) is dependent only on one independent variable(X).

Y is completely dependent on X.

Generally, Wife(Y) is completely dependent on Husband(X).

An ordinary differential equation (ODE) has only derivatives of one variable that is, it has no partial derivatives.

Here are a few examples of ODEs:

Three ordinary differential equations.

Y = f(X)

Partial Differential Equation:

One depedent variable(Y) is dependent at least two  variable(X) 

Generally WIfe & Childern & Grand pa/Ma is completely dependent on Father.

Wife, children & grand pa/ma are partially dependent on Father.

Y = F(X, Time, Temperature).

In contrast, a partial differential equation (PDE) has at least one partial derivative.

U = F(X, Y) U is partially dependent on X & Y.

V = f(X, T) U is partially dependent on X & T.

Here are a few examples of PDEs:

Several differential equations with at least one partial derivative

Industrial Example:

Mechanical property of Steel product = F(SoakingTime, Temperature, Phase transformation).

Mechanical property is partially dependent on soaking timransfore, temperature & phase transformation.

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Answered on 11/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

MANISH PAUL

Tutor

1,1.
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Answered on 02/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

Sarvajeet Kumar

An Experienced Trainer

y= -x+2tan(x/2)+C.
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Answered on 02/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

Determine order and degree of differential equation: [(d power 4)y] / [d(x power 4)] + sin y = 0?

Sarvajeet Kumar

An Experienced Trainer

4 & 1.
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Answered on 02/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

Solve with respect to x if y = (square of x) + 2x + c?

Sarvajeet Kumar

An Experienced Trainer

2x + 2.
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Answered on 02/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

Solve with respect to x: y = Ax?

Sarvajeet Kumar

An Experienced Trainer

A.
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Answered on 09/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

Define chain rule with respect to derivative?

Ankit

JEE/Board Maths Tutor

"If f is a function of g and g is a function of x, then the derivative of f with respect to x. is equal to the derivative of f(g) with respect to g. times the derivative of g(x) with respect to x.
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Answered on 02/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

Solve: y = x sin x?

Sarvajeet Kumar

An Experienced Trainer

dy/dx = sin x+x cos x.
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Answered on 04/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Differential Equations

Define differential equation?

Shiva K.

A differential equation is an equation which relates functions with their derivatives.
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