Internal problem ID [2934]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 186.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -y-\left (x^{2}-y^{2}\right ) f \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve(x*diff(y(x),x) = y(x)+(x^2-y(x)^2)*f(x),y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (\int f \relax (x )d x +c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.454 (sec). Leaf size: 36
DSolve[x y'[x]==y[x]+(x^2-y[x]^2)f[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \tanh \left (\int _1^x-f(K[1])dK[1]+c_1\right ) \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}