38.3.8 problem 8

Internal problem ID [6486]
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 : 8
Date solved : Wednesday, March 05, 2025 at 12:51:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+8*y(x) = 8*exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (8 x +c_1 -4\right ) {\mathrm e}^{4 x}}{2}+c_2 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-6*D[y[x],x]+8*y[x]==8*Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.224 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*y(x) - 8*exp(4*x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \left (C_{2} + 4 x\right ) e^{2 x}\right ) e^{2 x} \]