60.1.308 problem 309

Internal problem ID [10322]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 309
Date solved : Monday, January 27, 2025 at 07:08:38 PM
CAS classification : [_separable]

\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 113

dsolve((2*y(x)^3+y(x))*diff(y(x),x)-2*x^3-x = 0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} \\ y &= \frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} \\ y &= -\frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} \\ y &= \frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.425 (sec). Leaf size: 151

DSolve[-x - 2*x^3 + (y[x] + 2*y[x]^3)*D[y[x],x]==0,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*}