Internal problem ID [12054]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 18, The variation of constants formula. Exercises page 168
Problem number: 18.1 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (6 c_{1} {\mathrm e}^{5 x}-{\mathrm e}^{3 x}+6 c_{2} \right ) {\mathrm e}^{-2 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 29
DSolve[y''[x]-y'[x]-6*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {e^x}{6}+c_1 e^{-2 x}+c_2 e^{3 x} \]