Internal problem ID [3035]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 287.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-x \left (3 x^{2}-y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((x^2+1)*diff(y(x),x) = x*(3*x^2-y(x)),y(x), singsol=all)
\[ y \relax (x ) = x^{2}-2+\frac {c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 22
DSolve[(1+x^2)y'[x]==x(3 x^2-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\frac {c_1}{\sqrt {x^2+1}}-2 \\ \end{align*}