87.18.25 problem 25

Internal problem ID [23666]
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 : 25
Date solved : Thursday, October 02, 2025 at 09:44:04 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (\frac {1}{4}\right )&=0 \\ y^{\prime }\left (\frac {1}{4}\right )&={\frac {14}{9}} \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 20

ode:=2*x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-3*y(x) = 1/x^3; 
ic:=[y(1/4) = 0, D(y)(1/4) = 14/9]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 24 x^{{3}/{2}}-\frac {59}{36 x}+\frac {1}{18 x^{3}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 26

ode=2*x^2*D[y[x],{x,2}]+x*D[y[x],x]-3*y[x]==1/x^3; 
ic={y[1/4]==0,Derivative[1][y][1/4] ==14/9}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {864 x^{9/2}-59 x^2+2}{36 x^3} \end{align*}

✓ Sympy. Time used: 0.181 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - 3*y(x) - 1/x**3,0) 
ics = {y(1/4): 0, Subs(Derivative(y(x), x), x, 1/4): 14/9} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 24 x^{\frac {3}{2}} - \frac {59}{36 x} + \frac {1}{18 x^{3}} \]