ODE

• April 20th 2012, 01:59 AM
johnnys
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
• April 20th 2012, 03:43 AM
Prove It
Re: ODE
Quote:

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*}?
• April 21st 2012, 03:17 AM
johnnys
Re: ODE
yeah its supposed to be y'=y^2
• April 21st 2012, 03:22 AM
Prove It
Re: ODE
Quote:

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.