Internal problem ID [11162]
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`]]
\[ \boxed {6 y x +3 y^{2}+\left (2 x^{2}+3 y x \right ) y^{\prime }=-3 x^{2}} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) &= \frac {-4 c_{1} x^{2}-\sqrt {-2 c_{1}^{2} x^{4}+6}}{6 c_{1} x} \\ y \left (x \right ) &= \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: 2.7 (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*}