Internal problem ID [13394]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (2 y x +2 x^{2}\right ) y^{\prime }-2 y x -2 y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((2*x*y(x)+2*x^2)*diff(y(x),x)=x^2+2*x*y(x)+2*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (-1-\sqrt {1+\ln \left (x \right )+c_{1}}\right ) x \\ y \left (x \right ) &= \left (-1+\sqrt {1+\ln \left (x \right )+c_{1}}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.243 (sec). Leaf size: 42
DSolve[(2*x*y[x]+2*x^2)*y'[x]==x^2+2*x*y[x]+2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \left (1+\sqrt {\log (x)+1+2 c_1}\right ) \\ y(x)\to x \left (-1+\sqrt {\log (x)+1+2 c_1}\right ) \\ \end{align*}