Internal problem ID [2246]
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 35.
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+10 \sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)+diff(y(x),x)-2*y(x)=-10*sin(x),y(0) = 2, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x}+\cos \relax (x )+3 \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 17
DSolve[{y''[x]+y'[x]-2*y[x]==-10*Sin[x],{y[0]==2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x}+3 \sin (x)+\cos (x) \\ \end{align*}