6.10.24 problem 24

Internal problem ID [1828]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 24
Date solved : Tuesday, September 30, 2025 at 05:20:09 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \frac {15 c_2 \,x^{4}-4 x^{{5}/{2}}+15 c_1}{15 x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 27

ode=x^2*D[y[x],{x,2}]-x*D[y[x],x]-3*y[x]==x^(3/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {4 x^{3/2}}{15}+c_2 x^3+\frac {c_1}{x} \end{align*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} x^{4} - \frac {4 x^{\frac {5}{2}}}{15}}{x} \]