Internal problem ID [4114]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.21, page 231.
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 }-6 y-x -{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=x+exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-3 x} c_{1}+\frac {\left (180 x -36\right ) {\mathrm e}^{2 x}}{900}-\frac {x}{6}-\frac {1}{36} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 40
DSolve[y''[x]+y'[x]-6*y[x]==x+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{36} (-6 x-1)+c_1 e^{-3 x}+e^{2 x} \left (\frac {x}{5}-\frac {1}{25}+c_2\right ) \\ \end{align*}