Internal problem ID [3423]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 684.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y \left (2 y^{2}+1\right ) y^{\prime }-x \left (1+2 x^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 113
dsolve(y(x)*(1+2*y(x)^2)*diff(y(x),x) = x*(2*x^2+1),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1}+1}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1}+1}}}{2} \\ y \relax (x ) = -\frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1}+1}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1}+1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.362 (sec). Leaf size: 143
DSolve[y[x](1+2 y[x]^2)y'[x]==x(1+2 x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-1-\sqrt {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1-\sqrt {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-1+\sqrt {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1+\sqrt {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ \end{align*}