40.4.15 problem 19 (q)

Internal problem ID [6655]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (q)
Date solved : Monday, January 27, 2025 at 02:17:25 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ x -y^{2}-2-\sqrt {y^{2}+2}\, c_1 = 0 \]

✓ Solution by Mathematica

Time used: 5.572 (sec). Leaf size: 189

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

\begin{align*} y(x)\to -\frac {\sqrt {2 x-\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {2 x-\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {2 x+\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {2 x+\sqrt {4 c_1{}^2 x+c_1{}^4}-4+c_1{}^2}}{\sqrt {2}} \\ y(x)\to -i \sqrt {2} \\ y(x)\to i \sqrt {2} \\ \end{align*}