Internal problem ID [8131]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 551.
ODE order: 1.
ODE degree: 550.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{n}-f \relax (x )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}=0} \end {gather*}
✓ Solution by Maple
Time used: 2.499 (sec). Leaf size: 127
dsolve(diff(y(x),x)^n-f(x)^n*(y(x)-a)^(n+1)*(y(x)-b)^(n-1)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \relax (x )d x \right )+b \left (\int f \relax (x )d x \right )}\right )^{n} b}{-1+\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \relax (x )d x \right )+b \left (\int f \relax (x )d x \right )}\right )^{n}}-\frac {\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \relax (x )d x \right )+b \left (\int f \relax (x )d x \right )}\right )^{n} a}{-1+\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \relax (x )d x \right )+b \left (\int f \relax (x )d x \right )}\right )^{n}}+a \]
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 52
DSolve[-(f[x]^n*(-a + y[x])^(1 + n)*(-b + y[x])^(-1 + n)) + y'[x]^n==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a+\frac {n^n (b-a)}{n^n+(a-b)^n \left (\int _1^x-(-1)^{\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n} \\ \end{align*}