60.1.170 problem 171

Internal problem ID [10184]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 171
Date solved : Monday, January 27, 2025 at 06:34:14 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \end{align*}

✓ 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)
 

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

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 22

DSolve[x^3*D[y[x],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*}