73.5.19 problem 6.7 (g)

Internal problem ID [15130]
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)
Date solved : Tuesday, January 28, 2025 at 07:35:02 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (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 (-1-\sqrt {1+c_{1} +\ln \left (x \right )}\right ) x \\ y &= \left (-1+\sqrt {1+c_{1} +\ln \left (x \right )}\right ) x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.316 (sec). Leaf size: 42

DSolve[(2*x*y[x]+2*x^2)*D[y[x],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*}