I have three solutions for a non homogeneous, linear, 2nd order D.E
$$y_1(x)=3x−2x^2$$ $$y_2(x)=−2x^2+5xe^x$$ $$y_3(x)=2x−2x^2+3xe^x$$
I want to find the general solution.
I know that the general solution is a combination of the three but with some coefficients, $c_1y_1+c_2y_2+c_3y_3$ such that $c_1+c_2+c_3=1$.
How do i find the $c_1$, $c_2$, and $c_3$ coefficients, in order to calculate the general solution?