60.1.548 problem 551

Internal problem ID [10562]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 551
Date solved : Monday, January 27, 2025 at 09:05:24 PM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}&=0 \end{align*}

✓ Solution by Maple

Time used: 1.519 (sec). Leaf size: 55

dsolve(diff(y(x),x)^n-f(x)^n*(y(x)-a)^(n+1)*(y(x)-b)^(n-1)=0,y(x), singsol=all)
 

\[ y = \frac {b \left (-\frac {n}{\left (a -b \right ) \left (\int fd x +c_{1} \right )}\right )^{n}-a}{-1+\left (-\frac {n}{\left (a -b \right ) \left (\int fd x +c_{1} \right )}\right )^{n}} \]

✓ Solution by Mathematica

Time used: 23.971 (sec). Leaf size: 79

DSolve[-(f[x]^n*(-a + y[x])^(1 + n)*(-b + y[x])^(-1 + n)) + D[y[x],x]^n==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {b n^n+a (a-b)^n \left (\int _1^x-(-1)^{\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n}{n^n+(a-b)^n \left (\int _1^x-(-1)^{\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n} \]