Internal problem ID [8886]
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: 0.
CAS Maple gives this as type [_separable]
\[ \boxed {{y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}=0} \]
✓ Solution by Maple
Time used: 1.015 (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)
\[ y \left (x \right ) = -\frac {\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \left (x \right )d x \right )+b \left (\int f \left (x \right )d x \right )}\right )^{n} a}{-1+\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \left (x \right )d x \right )+b \left (\int f \left (x \right )d x \right )}\right )^{n}}+\frac {\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \left (x \right )d x \right )+b \left (\int f \left (x \right )d x \right )}\right )^{n} b}{-1+\left (\frac {n}{-c_{1} a +c_{1} b -a \left (\int f \left (x \right )d x \right )+b \left (\int f \left (x \right )d x \right )}\right )^{n}}+a \]
✓ Solution by Mathematica
Time used: 6.298 (sec). Leaf size: 79
DSolve[-(f[x]^n*(-a + y[x])^(1 + n)*(-b + y[x])^(-1 + n)) + y'[x]^n==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {b n^n+a (a-b)^n \left (\int _1^x-(-1)^{\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n}{n^n+(a-b)^n \left (\int _1^x-(-1)^{\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n} \]