How do you find all solutions of the differential equation #(d^2y)/(dx^2)=2x+1#?

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Answer 1 · 2017-01-10T13:30:30

# y=1/3x^3+1/2x^2 + Ax + B #

This is a Second Order non-homogeneous DE with constant coefficients, but separable so we can just integrate (twice):

# (d^2y)/(dx^2)=2x+1 #

Integrate:

# (dy)/(dx)=x^2+x + A #

Integrate again:

# y=1/3x^3+1/2x^2 + Ax + B #

which is the General Solution;