15.5.4 problem 4

Internal problem ID [2940]
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 : 4
Date solved : Monday, January 27, 2025 at 06:59:47 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {3 x^{2}}{3 c_1 \,x^{3}-1} \]

✓ Solution by Mathematica

Time used: 0.181 (sec). Leaf size: 26

DSolve[(x^2*y[x]+y[x]^2)+x^3*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {3 x^2}{-1+3 c_1 x^3} \\ y(x)\to 0 \\ \end{align*}