# How do you find all solutions of the differential equation #(d^2y)/(dx^2)=x^-2#?

##### 1 Answer

Dec 29, 2016

#### Explanation:

Note that when we integrate things like

Separating variables:

#d^2y=x^-2dx^2#

Integrating:

#intd^2y=intx^-2dx^2#

This is analogous to doing

#dy=(-x^-1+C_1)dx#

Integrating again:

#intdy=int(-1/x+C_1)dx#

Add another constant:

#y=-ln(absx)+C_1x+C_2#