Internal problem ID [2247]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-2 y-4 \cos \relax (x )+2 \sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+diff(y(x),x)-2*y(x)=4*cos(x)-2*sin(x),y(0) = -1, D(y)(0) = 4],y(x), singsol=all)
\[ y \relax (x ) = -\left (\left (\cos \relax (x )-\sin \relax (x )\right ) {\mathrm e}^{2 x}-{\mathrm e}^{3 x}+1\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 22
DSolve[{y''[x]+y'[x]-2*y[x]==4*Cos[x]-2*Sin[x],{y[0]==-1,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{-2 x}+e^x+\sin (x)-\cos (x) \\ \end{align*}