64.6.8 problem 8

Internal problem ID [13358]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 05:31:50 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} 2 x^{2}+y x +y^{2}+2 x^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 49

dsolve((2*x^2+x*y(x)+y(x)^2)+(2*x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\left (c_{1} x -\sqrt {c_{1} x}-2\right ) x}{c_{1} x -1} \\ y &= -\frac {\left (c_{1} x +\sqrt {c_{1} x}-2\right ) x}{c_{1} x -1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 38

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{(K[1]+1) (K[1]+2)}dK[1]=-\frac {\log (x)}{2}+c_1,y(x)\right ] \]