6.10.11 problem 11

Internal problem ID [1815]
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 : 11
Date solved : Tuesday, September 30, 2025 at 05:19:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{{5}/{2}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = x^(5/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{3}+c_1 \,x^{2}-4 x^{{5}/{2}} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 23

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==x^(5/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2 \left (-4 \sqrt {x}+c_2 x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.286 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**(5/2) + x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{2} + C_{2} x^{3} - 4 x^{\frac {5}{2}} \]