Internal problem ID [3128]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 380.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 63
dsolve(x^7*diff(y(x),x)+5*x^3*y(x)^2+2*(x^2+1)*y(x)^3 = 0,y(x), singsol=all)
\[ c_{1}+\frac {x}{\left (\left (\frac {1}{x}+\frac {x^{2}}{y \relax (x )}\right )^{2}+1\right )^{\frac {1}{4}}}+\frac {\left (x^{3}+y \relax (x )\right ) \hypergeom \left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (x^{3}+y \relax (x )\right )^{2}}{x^{2} y \relax (x )^{2}}\right )}{2 x y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 123
DSolve[x^7 y'[x]+5 x^3 y[x]^2+2(1+x^2)y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [c_1=\frac {\frac {1}{2} \sqrt [4]{1-\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2} \left (\frac {i x^2}{y(x)}+\frac {i}{x}\right ) \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2}},y(x)\right ] \]