60.1.569 problem 572

Internal problem ID [10583]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 572
Date solved : Monday, January 27, 2025 at 09:16:43 PM
CAS classification : [`x=_G(y,y')`]

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

✗ Solution by Maple

dsolve((x*diff(y(x),x)-y(x))^n*f(diff(y(x),x))+y(x)*g(diff(y(x),x))+x*h(diff(y(x),x))=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved