31.2.9 problem 10

Internal problem ID [5730]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 10
Date solved : Monday, January 27, 2025 at 01:11:42 PM
CAS classification : [_Riccati]

\begin{align*} \frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1}&=0 \end{align*}

✗ Solution by Maple

dsolve( x^n/(b*y(x)^2-c*x^(2*a))*diff(y(x),x) - a*y(x)*x^(a-1)/(b*y(x)^2-c*x^(2*a)) + x^(a-1)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[x^n/(b*y[x]^2-c*x^(2*a))*D[y[x],x] - a*y[x]*x^(a-1)/(b*y[x]^2-c*x^(2*a)) + x^(a-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved