Internal problem ID [7911]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 331.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {y^{\prime } f_{\nu }\relax (x ) \left (-y+y^{p +1}\right )}{-1+y}-\frac {g_{\nu }\relax (x ) \left (-y+y^{q +1}\right )}{-1+y}=0} \end {gather*}
✓ Solution by Maple
Time used: 15.313 (sec). Leaf size: 77
dsolve(diff(y(x),x)*f[nu](x)*(-y(x)+y(x)^(p+1))/(-1+y(x))-g[nu](x)*(-y(x)+y(x)^(q+1))/(-1+y(x)) = 0,y(x), singsol=all)
\[ \int \frac {g_{\nu }\relax (x )}{f_{\nu }\relax (x )}d x +\frac {y \relax (x )^{1+p} \Phi \left (-y \relax (x )^{q} \left (-1\right )^{\mathrm {csgn}\left (i y \relax (x )^{q}\right )}, 1, \frac {1+p}{q}\right )}{q}-\frac {y \relax (x ) \Phi \left (-y \relax (x )^{q} \left (-1\right )^{\mathrm {csgn}\left (i y \relax (x )^{q}\right )}, 1, \frac {1}{q}\right )}{q}+c_{1} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-Sum[y[x]^nu*g[nu][x], {nu, 1, q}] + Sum[y[x]^nu*f[nu][x], {nu, 1, p}]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved