Internal problem ID [8667]
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]
\[ \boxed {\frac {y^{\prime } f_{\nu }\left (x \right ) \left (-y+y^{p +1}\right )}{-1+y}-\frac {g_{\nu }\left (x \right ) \left (-y+y^{q +1}\right )}{-1+y}=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 78
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)
\[ \frac {y \left (x \right )^{p +1} \operatorname {LerchPhi}\left (-y \left (x \right )^{q} \left (-1\right )^{\operatorname {csgn}\left (i y \left (x \right )^{q}\right )}, 1, \frac {p +1}{q}\right )-y \left (x \right ) \operatorname {LerchPhi}\left (-y \left (x \right )^{q} \left (-1\right )^{\operatorname {csgn}\left (i y \left (x \right )^{q}\right )}, 1, \frac {1}{q}\right )+q \left (\int \frac {g_{\nu }\left (x \right )}{f_{\nu }\left (x \right )}d x +c_{1} \right )}{q} = 0 \]
✗ 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