32.4.6 problem 6

Internal problem ID [7779]
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 : 6
Date solved : Tuesday, September 30, 2025 at 05:05:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

ode:=diff(diff(y(x),x),x)-diff(y(x),x)+10*y(x) = 20-exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {39}\, x}{2}\right ) c_2 +{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {39}\, x}{2}\right ) c_1 +2-\frac {{\mathrm e}^{2 x}}{12} \]

✓ Mathematica. Time used: 0.492 (sec). Leaf size: 150

ode=D[y[x],{x,2}]-D[y[x],x]+10*y[x]==20-Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{x/2} \left (\cos \left (\frac {\sqrt {39} x}{2}\right ) \int _1^x\frac {2 e^{-\frac {K[2]}{2}} \left (-20+e^{2 K[2]}\right ) \sin \left (\frac {1}{2} \sqrt {39} K[2]\right )}{\sqrt {39}}dK[2]+\sin \left (\frac {\sqrt {39} x}{2}\right ) \int _1^x-\frac {2 e^{-\frac {K[1]}{2}} \left (-20+e^{2 K[1]}\right ) \cos \left (\frac {1}{2} \sqrt {39} K[1]\right )}{\sqrt {39}}dK[1]+c_2 \cos \left (\frac {\sqrt {39} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {39} x}{2}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) + exp(2*x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 20,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (\frac {\sqrt {39} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {39} x}{2} \right )}\right ) e^{\frac {x}{2}} - \frac {e^{2 x}}{12} + 2 \]