Internal problem ID [3451]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 713.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {2 x \left (x^{3}+y^{4}\right ) y^{\prime }-\left (x^{3}+2 y^{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 293
dsolve(2*x*(x^3+y(x)^4)*diff(y(x),x) = (x^3+2*y(x)^4)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\left (\left (16 c_{1}+8 x -8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ y \relax (x ) = \frac {\left (\left (16 c_{1}+8 x -8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ y \relax (x ) = -\frac {\left (\left (16 c_{1}+8 x +8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ y \relax (x ) = \frac {\left (\left (16 c_{1}+8 x +8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ y \relax (x ) = -\frac {i \left (\left (16 c_{1}+8 x -8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ y \relax (x ) = -\frac {i \left (\left (16 c_{1}+8 x +8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ y \relax (x ) = \frac {i \left (\left (16 c_{1}+8 x -8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ y \relax (x ) = \frac {i \left (\left (16 c_{1}+8 x +8 \sqrt {x^{2}+4 c_{1} x}\right ) x^{3} c_{1}^{3}\right )^{\frac {1}{4}}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.762 (sec). Leaf size: 166
DSolve[2 x(x^3+y[x]^4)y'[x]==(x^3+2 y[x]^4)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {c_1 x^2-x^{3/2} \sqrt {4+c_1{}^2 x}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {c_1 x^2-x^{3/2} \sqrt {4+c_1{}^2 x}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {x^{3/2} \sqrt {4+c_1{}^2 x}+c_1 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {x^{3/2} \sqrt {4+c_1{}^2 x}+c_1 x^2}}{\sqrt {2}} \\ y(x)\to 0 \\ \end{align*}