20.7.10 problem Problem 34

Internal problem ID [3725]
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
Date solved : Monday, January 27, 2025 at 07:56:18 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 0.022 (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)
 

\[ y \left (x \right ) = 8 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}+\left (3 x -4\right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

DSolve[{D[y[x],{x,2}]-y[x]==9*x*Exp[2*x],{y[0]==0,Derivative[1][y][0] ==7}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} (3 x-4)-4 e^{-x}+8 e^x \]