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 : Monday, January 27, 2025 at 09:46:42 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

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

DSolve[(1+x^2)D[y[x],x]==Tan[x]-2 x y[x],y[x],x,IncludeSingularSolutions -> True]
 

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