Internal problem ID [4101]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.6, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=sin(x),y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-2 x}-\frac {3 \cos \relax (x )}{10}+\frac {\sin \relax (x )}{10}+c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 32
DSolve[y''[x]+3*y'[x]+2*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} \left (\sin (x)-3 \cos (x)+10 e^{-2 x} \left (c_2 e^x+c_1\right )\right ) \\ \end{align*}