Internal problem ID [2245]
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 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-9 x \,{\mathrm e}^{2 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)-y(x)=9*x*exp(2*x),y(0) = 0, D(y)(0) = 7],y(x), singsol=all)
\[ y \relax (x ) = -4 \,{\mathrm e}^{-x}+8 \,{\mathrm e}^{x}+\left (3 x -4\right ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 29
DSolve[{y''[x]-y[x]==9*x*Exp[2*x],{y[0]==0,y'[0]==7}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} (3 x-4)-4 e^{-x}+8 e^x \\ \end{align*}