4.7.47 \(x^3 y'(x)=x^2 y(x)-x^2+3\)

ODE
\[ x^3 y'(x)=x^2 y(x)-x^2+3 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.006048 (sec), leaf count = 16

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

Maple
cpu = 0.011 (sec), leaf count = 14

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

DSolve[x^3*y'[x] == 3 - x^2 + x^2*y[x],y[x],x]

Mathematica raw output

{{y[x] -> 1 - x^(-2) + x*C[1]}}

Maple raw input

dsolve(x^3*diff(y(x),x) = 3-x^2+x^2*y(x), y(x),'implicit')

Maple raw output

y(x) = -1/x^2+1+_C1*x