15.2.6 problem 6

Internal problem ID [2876]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 6
Date solved : Monday, January 27, 2025 at 06:22:31 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 18

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

\[ y = \frac {x \left (\operatorname {LambertW}\left (c_1 x \right )+1\right )}{\operatorname {LambertW}\left (c_1 x \right )} \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 33

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

\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}-1\right )-\frac {1}{\frac {y(x)}{x}-1}=-\log (x)+c_1,y(x)\right ] \]