Internal problem ID [13406]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {2 y x +y^{2}+\left (2 y x +x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.062 (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 \left (x \right ) &= \frac {-c_{1}^{2} x^{2}+\sqrt {c_{1} x \left (c_{1}^{3} x^{3}+4\right )}}{2 c_{1}^{2} x} \\ y \left (x \right ) &= \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: 0.579 (sec). Leaf size: 118
DSolve[2*x*y[x]+y[x]^2+(2*x*y[x]+x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x-\frac {\sqrt {x^3+4 e^{c_1}}}{\sqrt {x}}\right ) \\ y(x)\to \frac {1}{2} \left (-x+\frac {\sqrt {x^3+4 e^{c_1}}}{\sqrt {x}}\right ) \\ y(x)\to -\frac {x^{3/2}+\sqrt {x^3}}{2 \sqrt {x}} \\ y(x)\to \frac {\sqrt {x^3}}{2 \sqrt {x}}-\frac {x}{2} \\ \end{align*}