38.3.2 problem 2

Internal problem ID [6480]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:07:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y&=10 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-4*y(x)=10*exp(3*x),y(x), singsol=all)
 

\[ y = \left (2 \,{\mathrm e}^{5 x}+c_2 \,{\mathrm e}^{4 x}+c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,2}]-4*y[x]==10*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (2 e^{5 x}+c_1 e^{4 x}+c_2\right ) \]