87.16.13 problem 13

Internal problem ID [23582]
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 : 13
Date solved : Thursday, October 02, 2025 at 09:43:10 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-8 y&=5+3 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=3*x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-8*y(x) = 3*x+5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{{8}/{3}} c_2 +\frac {c_1}{x}-\frac {5}{8}-\frac {3 x}{10} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 28

ode=3*x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-8*y[x]==3*x+5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^{8/3}-\frac {3 x}{10}+\frac {c_1}{x}-\frac {5}{8} \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) - 3*x - 8*y(x) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + C_{2} x^{\frac {8}{3}} - \frac {3 x}{10} - \frac {5}{8} \]