Internal problem ID [1980]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.3 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y \left (2 x^{2} y^{2}+1\right ) y^{\prime }+x \left (y^{4}+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 119
dsolve(y(x)*(2*x^2*y(x)^2+1)*diff(y(x),x)+x*(y(x)^4+1)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2-2 \sqrt {-4 x^{4}-8 x^{2} c_{1}+1}}}{2 x} \\ y \relax (x ) = \frac {\sqrt {-2-2 \sqrt {-4 x^{4}-8 x^{2} c_{1}+1}}}{2 x} \\ y \relax (x ) = -\frac {\sqrt {2}\, \sqrt {-1+\sqrt {-4 x^{4}-8 x^{2} c_{1}+1}}}{2 x} \\ y \relax (x ) = \frac {\sqrt {2}\, \sqrt {-1+\sqrt {-4 x^{4}-8 x^{2} c_{1}+1}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.233 (sec). Leaf size: 197
DSolve[y[x]*(2*x^2*y[x]^2+1)*y'[x]+x*(y[x]^4+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-\frac {1+\sqrt {-4 x^4+8 c_1 x^2+1}}{x^2}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\frac {1+\sqrt {-4 x^4+8 c_1 x^2+1}}{x^2}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\frac {-1+\sqrt {-4 x^4+8 c_1 x^2+1}}{x^2}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\frac {-1+\sqrt {-4 x^4+8 c_1 x^2+1}}{x^2}}}{\sqrt {2}} \\ y(x)\to -\sqrt [4]{-1} \\ y(x)\to \sqrt [4]{-1} \\ y(x)\to -(-1)^{3/4} \\ y(x)\to (-1)^{3/4} \\ \end{align*}