4.8.41 \(x^k y'(x)=a x^m+b y(x)^n\)

ODE
\[ x^k y'(x)=a x^m+b y(x)^n \] ODE Classification

[_Chini]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 20.8832 (sec), leaf count = 0 , could not solve

DSolve[x^k*Derivative[1][y][x] == a*x^m + b*y[x]^n, y[x], x]

Maple
cpu = 0.284 (sec), leaf count = 0 , could not solve

dsolve(x^k*diff(y(x),x) = a*x^m+b*y(x)^n, y(x),'implicit')

Mathematica raw input

DSolve[x^k*y'[x] == a*x^m + b*y[x]^n,y[x],x]

Mathematica raw output

DSolve[x^k*Derivative[1][y][x] == a*x^m + b*y[x]^n, y[x], x]

Maple raw input

dsolve(x^k*diff(y(x),x) = a*x^m+b*y(x)^n, y(x),'implicit')

Maple raw output

dsolve(x^k*diff(y(x),x) = a*x^m+b*y(x)^n, y(x),'implicit')