60.1.245 problem 246

Internal problem ID [10259]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 246
Date solved : Monday, January 27, 2025 at 06:42:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 63

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

\begin{align*} y &= \frac {-4 c_{1} x^{2}-\sqrt {-2 c_{1}^{2} x^{4}+6}}{6 c_{1} x} \\ y &= \frac {-4 c_{1} x^{2}+\sqrt {-2 c_{1}^{2} x^{4}+6}}{6 c_{1} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.823 (sec). Leaf size: 135

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

\begin{align*} y(x)\to -\frac {4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x} \\ y(x)\to \frac {-4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x} \\ y(x)\to -\frac {\sqrt {2} \sqrt {-x^4}+4 x^2}{6 x} \\ y(x)\to \frac {\sqrt {2} \sqrt {-x^4}-4 x^2}{6 x} \\ \end{align*}