40.4.10 problem 19 (k)

Internal problem ID [6650]
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 (k)
Date solved : Monday, January 27, 2025 at 02:16:54 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y \left (1+y^{2}\right )&=2 \left (1-2 x y^{2}\right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

dsolve(y(x)*(1+y(x)^2)=2*(1-2*x*y(x)^2)*diff(y(x),x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{4 \textit {\_Z}}-2 x \,{\mathrm e}^{2 \textit {\_Z}}+{\mathrm e}^{2 \textit {\_Z}}+c_1 +2 \textit {\_Z} -x \right )} \]

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 36

DSolve[y[x]*(1+y[x]^2)==2*(1-2*x*y[x]^2)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

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