62.10.1 problem Ex 1

Internal problem ID [12838]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 17. Other forms which Integrating factors can be found. Page 25
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:26:20 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 x^{2}+6 y x +3 y^{2}+\left (2 x^{2}+3 y x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 63

dsolve((3*x^2+6*x*y(x)+3*y(x)^2)+(2*x^2+3*x*y(x))*diff(y(x),x)=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: 1.815 (sec). Leaf size: 135

DSolve[(3*x^2+6*x*y[x]+3*y[x]^2)+(2*x^2+3*x*y[x])*D[y[x],x]==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*}