Internal problem ID [10148]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {3 x^{2}+6 y x +3 y^{2}+\left (2 x^{2}+3 y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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 \relax (x ) = \frac {-\frac {2 x^{2} c_{1}}{3}-\frac {\sqrt {-2 x^{4} c_{1}^{2}+6}}{6}}{c_{1} x} \\ y \relax (x ) = \frac {-\frac {2 x^{2} c_{1}}{3}+\frac {\sqrt {-2 x^{4} c_{1}^{2}+6}}{6}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.554 (sec). Leaf size: 135
DSolve[(3*x^2+6*x*y[x]+3*y[x]^2)+(2*x^2+3*x*y[x])*y'[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*}