29.11.1 problem 292

Internal problem ID [4892]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 292
Date solved : Sunday, March 30, 2025 at 04:09:18 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = \frac {-\ln \left (\cos \left (x \right )\right )+c_1}{x^{2}+1} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 21

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

\[ y(x)\to \frac {-\log (\cos (x))+c_1}{x^2+1} \]

✓ Sympy. Time used: 0.335 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {\log {\left (\frac {1}{\cos ^{2}{\left (x \right )}} \right )}}{2}}{x^{2} + 1} \]