Internal problem ID [10252]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of
undetermined coefficients. Page 107
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-3 \,{\mathrm e}^{2 x}+\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=3*exp(2*x)-cos(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+{\mathrm e}^{-x} x c_{1}+\frac {{\mathrm e}^{2 x}}{3}-\frac {\sin \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 34
DSolve[y''[x]+2*y'[x]+y[x]==3*Exp[2*x]-Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 x}}{3}-\frac {\sin (x)}{2}+e^{-x} (c_2 x+c_1) \\ \end{align*}