Internal problem ID [4118]
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 21.29, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y-5 \sin \left (x \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=5*sin(x),y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x}}{6}+\frac {{\mathrm e}^{2 x}}{3}+\frac {\cos \left (x \right )}{2}-\frac {3 \sin \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 30
DSolve[{y''[x]-y'[x]-2*y[x]==5*Sin[x],{y[0]==1,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (e^{-x}+2 e^{2 x}-9 \sin (x)+3 \cos (x)\right ) \\ \end{align*}