76.5.6 problem 6

Internal problem ID [17426]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 10:08:06 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.140 (sec). Leaf size: 21

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

\[ y = -\frac {x \left (1+\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-4 c_{1} -1}}{x^{4}}\right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 32

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

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