Question

X dx − y^2 dy = 0, y(0) = 1

Answer 1

`y=\sqrt[3]{3x^2+1}`

Explanation:

Given differential equation,

`xdx-y^2dy=0`

`\implies y^2dy=xdx`

Integrating both sides,

`\int y^2 dy=\int xdx`

`(y^3)/(3)=x^2+C`

We have, y(0) = 1,

That is, y = 1 when x = 0,

`\implies (1)/(3)=0+C\implies C = (1)/(3)`

`\implies (y^3)/(3)=x^2+(1)/(3)`

`y^3=3x^2+1`

`\implies y=\sqrt[3]{3x^2+1}`