29.24.22 problem 684

Internal problem ID [5275]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 684
Date solved : Monday, January 27, 2025 at 10:56:01 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.023 (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: 2.387 (sec). Leaf size: 151

DSolve[y[x]*(1+2*y[x]^2)*D[y[x],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*}