ODE
\[ y'(x)^n+x y'(x)-y(x)=0 \] ODE Classification
[_Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.155573 (sec), leaf count = 14
\[\left \{\left \{y(x)\to c_1{}^n+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.059 (sec), leaf count = 46
\[\left [y \left (x \right ) = -\left (\left (-\frac {x}{n}\right )^{\frac {1}{n -1}}\right )^{n} n +\left (\left (-\frac {x}{n}\right )^{\frac {1}{n -1}}\right )^{n}, y \left (x \right ) = \textit {\_C1}^{n}+\textit {\_C1} x\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + y'[x]^n == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + C[1]^n}}
Maple raw input
dsolve(diff(y(x),x)^n+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = -((-x/n)^(1/(n-1)))^n*n+((-x/n)^(1/(n-1)))^n, y(x) = _C1^n+_C1*x]