64.6.18 problem 18

Internal problem ID [13368]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 05:32:45 AM
CAS classification : [_exact, _rational]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.237 (sec). Leaf size: 87

dsolve([(3*x^2+2*x*y(x)^2)+(2*x^2*y(x)+6*y(x)^2)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {\left (1134-54 x^{3}-x^{6}+6 \sqrt {3 x^{9}+18 x^{6}-3402 x^{3}+35721}\right )^{{1}/{3}}}{6}+\frac {x^{4}}{6 \left (1134-54 x^{3}-x^{6}+6 \sqrt {3 x^{9}+18 x^{6}-3402 x^{3}+35721}\right )^{{1}/{3}}}-\frac {x^{2}}{6} \]

✓ Solution by Mathematica

Time used: 5.288 (sec). Leaf size: 103

DSolve[{(3*x^2+2*x*y[x]^2)+(2*x^2*y[x]+6*y[x]^2)*D[y[x],x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} \left (-x^2+\sqrt [3]{-x^6-54 x^3+6 \sqrt {3} \sqrt {x^9+6 x^6-1134 x^3+11907}+1134}+\frac {x^4}{\sqrt [3]{-x^6-54 x^3+6 \sqrt {3} \sqrt {x^9+6 x^6-1134 x^3+11907}+1134}}\right ) \]