15.8.8 problem 8

Internal problem ID [3011]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:07:45 AM
CAS classification : [_separable]

\begin{align*} 2 y+6&=x y y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 20

dsolve(2*(y(x)+3)=x*y(x)*diff(y(x),x),y(x), singsol=all)
 

\[ y = -3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-1-\frac {2 c_{1}}{3}}}{3 x^{{2}/{3}}}\right )-3 \]

✓ Solution by Mathematica

Time used: 18.614 (sec). Leaf size: 106

DSolve[2*(y[x]+3)==x*y[x]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -3 \left (1+W\left (\frac {1}{3} \sqrt [3]{-\frac {e^{-3-c_1}}{x^2}}\right )\right ) \\ y(x)\to -3 \left (1+W\left (-\frac {1}{3} \sqrt [3]{-1} \sqrt [3]{-\frac {e^{-3-c_1}}{x^2}}\right )\right ) \\ y(x)\to -3 \left (1+W\left (\frac {1}{3} (-1)^{2/3} \sqrt [3]{-\frac {e^{-3-c_1}}{x^2}}\right )\right ) \\ y(x)\to -3 \\ \end{align*}