Internal problem ID [3603]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 347.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Riccati]
\[ \boxed {y^{\prime } x^{3}-\left (y-1\right ) x^{2}-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(x^3*diff(y(x),x) = x^2*(y(x)-1)+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left (\frac {c_{1} x -1}{x}\right ) x \]
✓ Solution by Mathematica
Time used: 0.713 (sec). Leaf size: 51
DSolve[x^3 y'[x]==x^2(y[x]-1)+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \left (e^{2/x}-e^{2 c_1}\right )}{e^{2/x}+e^{2 c_1}} y(x)\to -x y(x)\to x \end{align*}