87.18.14 problem 14

Internal problem ID [23655]
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 : 14
Date solved : Thursday, October 02, 2025 at 09:43:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=x^{{1}/{4}} \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-4*y(x) = x^(1/4)*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{4}}+c_1 x -\frac {16 x^{{1}/{4}} \left (51 \ln \left (x \right )+56\right )}{2601} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 31

ode=x^2*D[y[x],{x,2}]+4*x*D[y[x],x]-4*y[x]==x^(1/4)*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^4}-\frac {16 \sqrt [4]{x} (51 \log (x)+56)}{2601}+c_2 x \end{align*}

✓ Sympy. Time used: 0.197 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{4}} + C_{2} x - \frac {16 \sqrt [4]{x} \log {\left (x \right )}}{51} - \frac {896 \sqrt [4]{x}}{2601} \]