Internal problem ID [4679]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number: Problem 12.4.
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-{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_{1}+\frac {{\mathrm e}^{3 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[y''[x]-y'[x]-2*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{3 x}}{4}+c_1 e^{-x}+c_2 e^{2 x} \\ \end{align*}