Internal problem ID [3040]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 292.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-\tan \relax (x )+2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 19
dsolve((x^2+1)*diff(y(x),x) = tan(x)-2*x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-\ln \left (\cos \relax (x )\right )+c_{1}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 21
DSolve[(1+x^2)y'[x]==Tan[x]-2 x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-\log (\cos (x))+c_1}{x^2+1} \\ \end{align*}