Thread: ODE

**johnnys** · April 20th 2012, 01:59 AM

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

**Prove It** · April 20th 2012, 03:43 AM

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

**johnnys** · April 21st 2012, 03:17 AM

yeah its supposed to be y'=y^2

**Prove It** · April 21st 2012, 03:22 AM

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.

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