Internal problem ID [5307]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y \left (y^{2}+1\right )-2 \left (1-2 x y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.176 (sec). Leaf size: 36
DSolve[y[x]*(1+y[x]^2)==2*(1-2*x*y[x]^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {y(x)^2+2 \log (y(x))}{\left (y(x)^2+1\right )^2}+\frac {c_1}{\left (y(x)^2+1\right )^2},y(x)\right ] \]