87.16.9 problem 9

Internal problem ID [23578]
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 : 9
Date solved : Thursday, October 02, 2025 at 09:43:08 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=x^{2} {\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = x^2*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} \left (c_2 +c_1 x +\frac {1}{12} x^{4}\right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==x^2*Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{12} e^{5 x} \left (x^4+12 c_2 x+12 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*exp(5*x) + 25*y(x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + \frac {x^{3}}{12}\right )\right ) e^{5 x} \]