20.9.8 problem Problem 8

Internal problem ID [3752]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 8
Date solved : Sunday, March 30, 2025 at 02:07:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=\frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = 2*exp(5*x)/(x^2+4); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 34

ode=D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==2*Exp[5*x]/(4+x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{5 x} \left (x \arctan \left (\frac {x}{2}\right )-\log \left (x^2+4\right )+c_2 x+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 2*exp(5*x)/(x**2 + 4),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (25*x**2*y(x) + x**2*Derivative(y(x), (x, 2)) + 100*y(x) - 2*exp(5*x) + 4*Derivative(y(x), (x, 2)))/(10*(x**2 + 4)) cannot be solved by the factorable group method