62.8.2 problem Ex 2

Internal problem ID [12830]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 15. Page 22
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:25:52 AM
CAS classification : [_separable]

\begin{align*} y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 31

dsolve(y(x)^2*(3*y(x)-6*x*diff(y(x),x))-x*(y(x)-2*x*diff(y(x),x))=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {3}\, \sqrt {x}}{3} \\ y &= \frac {\sqrt {3}\, \sqrt {x}}{3} \\ y &= \sqrt {x}\, c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.676 (sec). Leaf size: 78

DSolve[y[x]^2*(3*y[x]-6*x*D[y[x],x])- x*(4*y[x]-2*x*D[y[x],x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i \sqrt {x} \sqrt {W\left (-3 e^{-4-3 c_1} x^3\right )}}{\sqrt {3}} \\ y(x)\to \frac {i \sqrt {x} \sqrt {W\left (-3 e^{-4-3 c_1} x^3\right )}}{\sqrt {3}} \\ y(x)\to 0 \\ \end{align*}