Internal problem ID [2836]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page
575
Problem number: Problem 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-3 y=5 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+2*diff(y(x),x)-3*y(x)=5*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (5 x +4 c_{1} \right ) {\mathrm e}^{-3 x} {\mathrm e}^{4 x}}{4}+{\mathrm e}^{-3 x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 29
DSolve[y''[x]+2*y'[x]-3*y[x]==5*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-3 x}+e^x \left (\frac {5 x}{4}-\frac {5}{16}+c_2\right ) \]