Internal problem ID [235]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 32.
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-{\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(x),y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left ({\mathrm e}^{3 x}+15 \,{\mathrm e}^{x}-16\right ) {\mathrm e}^{-2 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 26
DSolve[{y''[x]+3*y'[x]+2*y[x]==Exp[x],{y[0]==0,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-2 x} \left (15 e^x+e^{3 x}-16\right ) \\ \end{align*}