4.7.30 \(2 x^2 y'(x)=y(x)\)

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00324911 (sec), leaf count = 17

\[\left \{\left \{y(x)\to c_1 e^{\left .-\frac {1}{2}\right /x}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 12

\[ \left \{ y \relax (x ) ={\it \_C1}\,{{\rm e}^{-{\frac {1}{2\,x}}}} \right \} \] Mathematica raw input

DSolve[2*x^2*y'[x] == y[x],y[x],x]

Mathematica raw output

{{y[x] -> C[1]/E^(1/(2*x))}}

Maple raw input

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

Maple raw output

y(x) = _C1*exp(-1/2/x)