60.1.307 problem 308

Internal problem ID [10321]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 308
Date solved : Monday, January 27, 2025 at 07:08:34 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 37

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

\begin{align*} y &= 0 \\ y &= -\frac {\sqrt {-2 x^{2}+4 c_{1}}}{2} \\ y &= \frac {\sqrt {-2 x^{2}+4 c_{1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 53

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

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