1.170 problem 171

Internal problem ID [7751]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 171.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {x^{3} y^{\prime }-y^{2}-y x^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^3*diff(y(x),x) - y(x)^2 - x^2*y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{2}}{c_{1} x +1} \]

Solution by Mathematica

Time used: 0.15 (sec). Leaf size: 22

DSolve[x^3*y'[x] - y[x]^2 - x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2}{1+c_1 x} \\ y(x)\to 0 \\ \end{align*}