15.5.7 problem 7

Internal problem ID [2943]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 7
Date solved : Monday, January 27, 2025 at 06:59:56 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} y \left (y-x^{2}\right )+x^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

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

\[ y = \frac {x^{2}}{c_1 x -1} \]

✓ Solution by Mathematica

Time used: 0.164 (sec). Leaf size: 22

DSolve[y[x]*(y[x]-x^2)+x^3*D[y[x],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*}