Internal problem ID [3109]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 361.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (x^{2}+1\right ) y^{\prime }-2+4 x^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*(x^2+1)*diff(y(x),x) = 2-4*x^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}+2 \ln \relax (x )+c_{1}}{\left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 23
DSolve[x(1+x^2)y'[x]==2(1-2 x^2 y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+2 \log (x)+c_1}{\left (x^2+1\right )^2} \\ \end{align*}