Internal problem ID [4655]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page
95
Problem number: Problem 11.1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-2 y-4 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=4*x^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_{1}-2 x^{2}+2 x -3 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 29
DSolve[y''[x]-y'[x]-2*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 (x-1) x+c_1 e^{-x}+c_2 e^{2 x}-3 \\ \end{align*}