Internal problem ID [5634]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 3(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-2 x +1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=2*x-1,y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{-x}+x -2 \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 23
DSolve[y''[x]+3*y'[x]+2*y[x]==2*x-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+e^{-2 x} \left (c_2 e^x+c_1\right )-2 \\ \end{align*}