15.8.25 problem 26

Internal problem ID [3028]
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 : 26
Date solved : Monday, January 27, 2025 at 07:09:26 AM
CAS classification : [_separable]

\begin{align*} 3 x -6&=x y y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 31

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

\begin{align*} y &= \sqrt {-12 \ln \left (x \right )+c_{1} +6 x} \\ y &= -\sqrt {-12 \ln \left (x \right )+c_{1} +6 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 50

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

\begin{align*} y(x)\to -\sqrt {2} \sqrt {3 x-6 \log (x)+c_1} \\ y(x)\to \sqrt {2} \sqrt {3 x-6 \log (x)+c_1} \\ \end{align*}