Internal problem ID [10248]
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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y-3 \,{\mathrm e}^{2 x}+\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} x c_{1} +\frac {{\mathrm e}^{2 x}}{3}-\frac {\sin \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.142 (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*}