64.4.20 problem 20

Internal problem ID [13309]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 05:17:42 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 x^{2}+9 y x +5 y^{2}-\left (6 x^{2}+4 y x \right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.511 (sec). Leaf size: 21

dsolve([(3*x^2+9*x*y(x)+5*y(x)^2)-(6*x^2+4*x*y(x))*diff(y(x),x)=0,y(2) = -6],y(x), singsol=all)
 

\[ y = -\frac {\left (3+\sqrt {-3+6 \sqrt {x}\, \sqrt {2}}\right ) x}{2} \]

✓ Solution by Mathematica

Time used: 20.489 (sec). Leaf size: 30

DSolve[{(3*x^2+9*x*y[x]+5*y[x]^2)-(6*x^2+4*x*y[x])*D[y[x],x]==0,{y[2]==-6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} \left (\sqrt {6 \sqrt {2} \sqrt {x}-3}+3\right ) x \]