38.4.8 problem 8

Internal problem ID [6494]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 8
Date solved : Monday, January 27, 2025 at 02:08:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x +{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

\[ y = {\mathrm e}^{x} c_2 +{\mathrm e}^{3 x} c_1 -{\mathrm e}^{2 x}+\frac {x}{3}+\frac {4}{9} \]

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 35

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

\[ y(x)\to \frac {x}{3}-e^{2 x}+c_1 e^x+c_2 e^{3 x}+\frac {4}{9} \]