73.7.31 problem 31

Internal problem ID [15189]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 07:40:47 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x y y^{\prime }&=x^{2}+y x +y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.105 (sec). Leaf size: 22

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

\[ y = x \left (-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1} -1}}{x}\right )-1\right ) \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 30

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

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