4.6.2 \(x^2 y'(x)=a-y(x)\)

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0059408 (sec), leaf count = 15

\[\left \{\left \{y(x)\to a+c_1 e^{\frac {1}{x}}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 12

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

DSolve[x^2*y'[x] == a - y[x],y[x],x]

Mathematica raw output

{{y[x] -> a + E^x^(-1)*C[1]}}

Maple raw input

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

Maple raw output

y(x) = a+exp(1/x)*_C1