Question

solutions of differential equation dy/dx = x square / y square is

Answer 1

Please see the attachment

Answer 2

Answer:

The solution of the given differential equation is

$y {}^{3} = {x}^{3} + C$

Step-by-step explanation:

The given differential equation is

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

On cross multiplication,we get

${y}^{2} dy = {x}^{2} dx$

Integrating on both the sides,we get

$\int {y}^{2} dy = \int {x}^{2} dx$

We have a basic formula of integration which is

$\int {x}^{n} dx = \frac{ {x}^{n + 1} }{n + 1} + c$

Using this,we get

$\frac{ {y}^{3} }{3} = \frac{ {x}^{3} }{3} + c \\ = > {y}^{3} = x {}^{3} + 3c \\ = > {y}^{3} = x {}^{3} + C$

Hence,the solution of the given differential equation is

$y {}^{3} = {x}^{3} + C$

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