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Lesson Posted on 27/12/2017 Differential Equations

Ordinary & Partial Differential Equation

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

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:

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:

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

Determine order and degree of differential equation: dy/dx + 5y = 0?

MANISH PAUL

Tutor

1,1.

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Answers 4 Comments Answered on 02/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Differential Equations

Solve with respect to x: dy / dx = (1 - cos x) / (1 + cos x)?

Sarvajeet Kumar

An Experienced Trainer

y= -x+2tan(x/2)+C.

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Answers 3 Comments Answered on 02/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics 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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Answers 2 Comments Answered on 02/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics 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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Solve with respect to x: y = cos x + c?

Sarvajeet Kumar

An Experienced Trainer

-sinx.

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Solve with respect to sin x: y = sin x / tan x + cos x + c?

Sarvajeet Kumar

An Experienced Trainer

-2tan x.

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Answers 2 Comments Answered on 09/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics 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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Solve: y = x sin x?

Sarvajeet Kumar

An Experienced Trainer

dy/dx = sin x+x cos x.

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Answers 1 Comments Answered on 04/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Differential Equations

Define differential equation?

Shiva K.

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

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