Internal problem ID [13418]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.5 (e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.859 (sec). Leaf size: 137
dsolve(3*y(x)+3*y(x)^2+(2*x+4*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-c_{1} x -\sqrt {c_{1}^{2} x^{2}-4 \sqrt {c_{1} x}}}{2 c_{1} x} \\ y \left (x \right ) &= \frac {-c_{1} x +\sqrt {c_{1}^{2} x^{2}-4 \sqrt {c_{1} x}}}{2 c_{1} x} \\ y \left (x \right ) &= \frac {-c_{1} x -\sqrt {c_{1}^{2} x^{2}+4 \sqrt {c_{1} x}}}{2 c_{1} x} \\ y \left (x \right ) &= \frac {-c_{1} x +\sqrt {c_{1}^{2} x^{2}+4 \sqrt {c_{1} x}}}{2 c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.61 (sec). Leaf size: 67
DSolve[3*y[x]+3*y[x]^2+(2*x+4*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-1-\sqrt {1+\frac {4 e^{c_1}}{x^{3/2}}}\right ) \\ y(x)\to \frac {1}{2} \left (-1+\sqrt {1+\frac {4 e^{c_1}}{x^{3/2}}}\right ) \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}