73.6.3 problem 7.4 (a)

Internal problem ID [15142]
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 : 7.4 (a)
Date solved : Tuesday, January 28, 2025 at 07:36:38 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 71

dsolve(2*x*y(x)+y(x)^2+(2*x*y(x)+x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-c_{1}^{2} x^{2}+\sqrt {c_{1} x \left (c_{1}^{3} x^{3}+4\right )}}{2 c_{1}^{2} x} \\ y &= \frac {-c_{1}^{2} x^{2}-\sqrt {c_{1} x \left (c_{1}^{3} x^{3}+4\right )}}{2 c_{1}^{2} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 40

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {2 K[1]+1}{K[1] (K[1]+1)}dK[1]=-3 \log (x)+c_1,y(x)\right ] \]