4.3.47 \(x^2+x y'(x)-y(x)=0\)

ODE
\[ x^2+x y'(x)-y(x)=0 \] ODE Classification

[_linear]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.00314319 (sec), leaf count = 13

\[\left \{\left \{y(x)\to x \left (c_1-x\right )\right \}\right \}\]

Maple
cpu = 0.004 (sec), leaf count = 11

\[ \left \{ y \relax (x ) = \left (-x+{\it \_C1} \right ) x \right \} \] Mathematica raw input

DSolve[x^2 - y[x] + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x*(-x + C[1])}}

Maple raw input

dsolve(x*diff(y(x),x)+x^2-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (-x+_C1)*x