Internal problem ID [3931]
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]
\[ \boxed {y \left (1+2 y^{2}\right ) y^{\prime }=x \left (2 x^{2}+1\right )} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = -\frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} y \left (x \right ) = \frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} y \left (x \right ) = -\frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} y \left (x \right ) = \frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 2.383 (sec). Leaf size: 151
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 {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} y(x)\to \frac {\sqrt {-1-\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} y(x)\to -\frac {\sqrt {-1+\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} y(x)\to \frac {\sqrt {-1+\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} \end{align*}