87.16.7 problem 7

Internal problem ID [23576]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:43:05 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-13 y^{\prime }+36 y&=x \,{\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-13*diff(y(x),x)+36*y(x) = x*exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{4 x} \left (x^{2}-10 c_2 \,{\mathrm e}^{5 x}+\frac {2 x}{5}-10 c_1 \right )}{10} \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 37

ode=D[y[x],{x,2}]-13*D[y[x],x]+36*y[x]==x*Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 e^{9 x}-\frac {1}{250} e^{4 x} \left (25 x^2+10 x+2-250 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.168 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(4*x) + 36*y(x) - 13*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{5 x} - \frac {x^{2}}{10} - \frac {x}{25}\right ) e^{4 x} \]