52.2.24 problem 25

Internal problem ID [10447]
Book : Second order enumerated odes
Section : section 2
Problem number : 25
Date solved : Tuesday, September 30, 2025 at 07:27:13 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=x^{5} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=x*diff(diff(y(x),x),x)-diff(y(x),x)+4*x^3*y(x) = x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x^{2}\right ) c_2 +\cos \left (x^{2}\right ) c_1 +\frac {x^{2}}{4} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 68

ode=x*D[y[x],{x,2}]-D[y[x],x]+4*x^3*y[x]==x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sin \left (x^2\right ) \int _1^x\frac {1}{2} \cos \left (K[1]^2\right ) K[1]^3dK[1]-\frac {1}{8} \sin \left (2 x^2\right )+\frac {1}{4} x^2 \cos ^2\left (x^2\right )+c_1 \cos \left (x^2\right )+c_2 \sin \left (x^2\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5 + 4*x**3*y(x) + x*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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