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 = 41.558 (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 = 0.257 (sec), leaf count = 0 , could not solve
dsolve(x^k*diff(y(x),x) = a*x^m+b*y(x)^n, y(x))
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))
Maple raw output
dsolve(x^k*diff(y(x),x) = a*x^m+b*y(x)^n, y(x))