Internal problem ID [3442]
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]
\[ \boxed {x y^{\prime }-y-\left (x^{2}-y^{2}\right ) f \left (x \right )=0} \]
✓ 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)
\[ y \left (x \right ) = \tanh \left (\int f \left (x \right )d x +c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.384 (sec). Leaf size: 65
DSolve[x y'[x]==y[x]+(x^2-y[x]^2)f[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-x \exp \left (2 \left (\int _1^x-f(K[1])dK[1]+c_1\right )\right )}{1+\exp \left (2 \left (\int _1^x-f(K[1])dK[1]+c_1\right )\right )} y(x)\to -x y(x)\to x \end{align*}