60.1.330 problem 331

Internal problem ID [10344]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 331
Date solved : Monday, January 27, 2025 at 07:17:30 PM
CAS classification : [_separable]

\begin{align*} \frac {y^{\prime } f_{\nu }\left (x \right ) \left (-y+y^{p +1}\right )}{y-1}-\frac {g_{\nu }\left (x \right ) \left (-y+y^{q +1}\right )}{y-1}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.161 (sec). Leaf size: 76

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)
 

\[ \frac {y^{p +1} \operatorname {LerchPhi}\left (-y^{q} \left (-1\right )^{\operatorname {csgn}\left (i y^{q}\right )}, 1, \frac {p +1}{q}\right )-y \operatorname {LerchPhi}\left (-y^{q} \left (-1\right )^{\operatorname {csgn}\left (i y^{q}\right )}, 1, \frac {1}{q}\right )+q \left (\int \frac {g_{\nu }\left (x \right )}{f_{\nu }\left (x \right )}d x +c_{1} \right )}{q} = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (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}]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved