20.9.23 problem Problem 23

Internal problem ID [3767]
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 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 23
Date solved : Monday, January 27, 2025 at 08:01:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-9 y&=F \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 47

dsolve(diff(y(x),x$2)-9*y(x)=F(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-3 x} c_{2} +c_{1} {\mathrm e}^{3 x}+\frac {\left (\int {\mathrm e}^{-3 x} F \left (x \right )d x \right ) {\mathrm e}^{3 x}}{6}-\frac {\left (\int {\mathrm e}^{3 x} F \left (x \right )d x \right ) {\mathrm e}^{-3 x}}{6} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 66

DSolve[D[y[x],{x,2}]-y[x]==F[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{2 x} \int _1^x\frac {1}{2} e^{-K[1]} F(K[1])dK[1]+\int _1^x-\frac {1}{2} e^{K[2]} F(K[2])dK[2]+c_1 e^{2 x}+c_2\right ) \]