# Thread: how do i solve this second order differential equation?

1. ## how do i solve this second order differential equation?

please could someone explain how to solve this second order differential equation. I know how to do it when it has a first order term as well, but in this case that term equals zero. so need to solve this...

$\displaystyle 1/2f''(x)y^2=0$

Thanks

2. Originally Posted by willowtree
please could someone explain how to solve this second order differential equation. I know how to do it when it has a first order term as well, but in this case that term equals zero. so need to solve this...

$\displaystyle 1/2f''(x)y^2=0$

Thanks
I take it that this is actually

$\displaystyle \frac{1}{2}\cdot \frac{d^2y}{dx^2}\cdot y^2 = 0$.

It should be easy to see that either $\displaystyle \frac{d^2y}{dx^2} = 0$ or $\displaystyle y^2 = 0$.

Case 1:

$\displaystyle \frac{d^2y}{dx^2} = 0$

$\displaystyle \frac{dy}{dx} = C_1$

$\displaystyle y = C_1x + C_2$.

Case 2:

$\displaystyle y^2 = 0$

$\displaystyle y = 0$.