87.16.8 problem 8

Internal problem ID [23577]
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 119
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:43:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

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

\[ y = x \left (\int \frac {\tan \left (x \right )}{x^{3}}d x x +c_2 x -\int \frac {\tan \left (x \right )}{x^{2}}d x +c_1 \right ) \]

✓ Mathematica. Time used: 3.076 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.808 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} x + x \int \frac {\tan {\left (x \right )}}{x^{3}}\, dx - \int \frac {\tan {\left (x \right )}}{x^{2}}\, dx\right ) \]