Internal problem ID [4701]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page
248
Problem number: Problem 24.32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+5 y-3 \,{\mathrm e}^{-2 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 31
dsolve([diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=3*exp(-2*x),y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (4 \cos \left (2 x \right )+13 \sin \left (2 x \right )\right ) {\mathrm e}^{-x}}{10}+\frac {3 \,{\mathrm e}^{-2 x}}{5} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 33
DSolve[{y''[x]+2*y'[x]+5*y[x]==3*Exp[-2*x],{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} e^{-2 x} \left (e^x (13 \sin (2 x)+4 \cos (2 x))+6\right ) \\ \end{align*}