73.6.15 problem 7.5 (e)

Internal problem ID [15154]
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)
Date solved : Tuesday, January 28, 2025 at 07:38:28 AM
CAS classification : [_separable]

\begin{align*} 3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 1.865 (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 &= \frac {-c_{1} x -\sqrt {c_{1}^{2} x^{2}-4 \sqrt {c_{1} x}}}{2 c_{1} x} \\ y &= \frac {-c_{1} x +\sqrt {c_{1}^{2} x^{2}-4 \sqrt {c_{1} x}}}{2 c_{1} x} \\ y &= \frac {-c_{1} x -\sqrt {c_{1}^{2} x^{2}+4 \sqrt {c_{1} x}}}{2 c_{1} x} \\ y &= \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: 0.400 (sec). Leaf size: 51

DSolve[3*y[x]+3*y[x]^2+(2*x+4*x*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {2 K[1]+1}{K[1] (K[1]+1)}dK[1]\&\right ]\left [-\frac {3 \log (x)}{2}+c_1\right ] \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}