87.18.7 problem 7

Internal problem ID [23648]
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 135
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:43:48 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&={\mathrm e}^{6 x} \ln \left (x \right ) \end{align*}

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

ode:=diff(diff(y(x),x),x)-12*diff(y(x),x)+36*y(x) = exp(6*x)*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{6 x} \left (c_2 +c_1 x +\frac {x^{2} \left (2 \ln \left (x \right )-3\right )}{4}\right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 36

ode=D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==Exp[6*x]*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} e^{6 x} \left (-3 x^2+2 x^2 \log (x)+4 c_2 x+4 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.213 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) - exp(6*x)*log(x) - 12*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + \frac {x \log {\left (x \right )}}{2} - \frac {3 x}{4}\right )\right ) e^{6 x} \]