- #1

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xy^2dy/dx + y = x^2

i tried to solve it by using linear first order differential equation technique and also by using different exact and reducable exact differential equaions... help me

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- Thread starter suryanarayan
- Start date

- #1

- 20

- 0

xy^2dy/dx + y = x^2

i tried to solve it by using linear first order differential equation technique and also by using different exact and reducable exact differential equaions... help me

- #2

Simon Bridge

Science Advisor

Homework Helper

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Rewriting:

$$\frac{dy}{dx} = \frac{x^2-y}{xy^2} = \frac{x}{y^2}-\frac{1}{xy}$$

... hmmmm... what have you tried?

... in what context does it show up?

- #3

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Hi !

The ODEs of the kind : dY/dX = f(X)*Y^p + g(X)

are close to the Bernoulli ODE : dY/dX = f(X)*Y^p + g(X)*Y

where p is not an integer.

While we know how to analytically solve the Bernoulli ODE, we don't know to solve dY/dX = f(X)*Y^p + g(X) in the general case.

The question here is to solve the ODE in the case: p=1/3 , f(x)=-3/2X , g(x)=2/3 (see attachment)

As far as I know, if g(x)=constant (not 0) the ODE is not analytically solvable.

So, a numerical method of solving will be required.

The ODEs of the kind : dY/dX = f(X)*Y^p + g(X)

are close to the Bernoulli ODE : dY/dX = f(X)*Y^p + g(X)*Y

where p is not an integer.

While we know how to analytically solve the Bernoulli ODE, we don't know to solve dY/dX = f(X)*Y^p + g(X) in the general case.

The question here is to solve the ODE in the case: p=1/3 , f(x)=-3/2X , g(x)=2/3 (see attachment)

As far as I know, if g(x)=constant (not 0) the ODE is not analytically solvable.

So, a numerical method of solving will be required.

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