Question

Isnt there a simple substitution to solve
y''=y'+2x

Answer 1

if you know y prime you can substitute it....

Answer 2

that is the entire problem, I was talking about a linear transformation of a non-linear DE

Answer 3

sorry, I haven't studied DE in a long time. perhaps someone else might be able to answer

Answer 4

Substitute \[ y=e^{ax} \]

Answer 5

In the complementary solution. The particular solution can be obtained with undetermined coefficients.

Answer 6

\[y(x)=c_1 e^x+c_2-x^2-2 x \]

Answer 7

y'=v so that y''=v' then solve the linear ODE for v then integrate the answer to get y=-x^2-2x-c1e^-x +c2