1. ## ODE

i am refreshing my knowledge and theory on ode's and i have noticed that i have pretty much forgotten a lot of stuff.
Can some one give me a few pointers for making substitutions for solving non linear first order and second order sdes

Eg y(x)=y(x)^2
y(0)=1

2. ## Re: ODE

Originally Posted by johnnys
i am refreshing my knowledge and theory on ode's and i have noticed that i have pretty much forgotten a lot of stuff.
Can some one give me a few pointers for making substitutions for solving non linear first order and second order sdes

Eg y(x)=y(x)^2
y(0)=1
What you have written is not a DE.

Did you mean \displaystyle \begin{align*} \frac{dy}{dx} = y^2 \end{align*}?

3. ## Re: ODE

yeah its supposed to be y'=y^2

4. ## Re: ODE

Originally Posted by johnnys
yeah its supposed to be y'=y^2
That equation is separable.

\displaystyle \begin{align*} \frac{dy}{dx} &= y^2 \\ y^{-2}\,\frac{dy}{dx} &= 1 \\ \int{y^{-2}\,\frac{dy}{dx}\,dx} &= \int{1\,dx} \\ \int{y^{-2}\,dy} &= \int{1\,dx} \end{align*}

Go from here.