4.8.15 \(x \left (x^2+1\right ) y'(x)=x-\left (5 x^2+3\right ) y(x)\)

ODE
\[ x \left (x^2+1\right ) y'(x)=x-\left (5 x^2+3\right ) y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0102446 (sec), leaf count = 26

\[\left \{\left \{y(x)\to \frac {4 c_1+x^4}{4 \left (x^5+x^3\right )}\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 22

\[ \left \{ y \relax (x ) ={\frac {1}{ \left ({x}^{2}+1 \right ) {x}^{3}} \left ({\frac {{x}^{4}}{4}}+{\it \_C1} \right ) } \right \} \] Mathematica raw input

DSolve[x*(1 + x^2)*y'[x] == x - (3 + 5*x^2)*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (x^4 + 4*C[1])/(4*(x^3 + x^5))}}

Maple raw input

dsolve(x*(x^2+1)*diff(y(x),x) = x-(5*x^2+3)*y(x), y(x),'implicit')

Maple raw output

y(x) = (1/4*x^4+_C1)/(x^2+1)/x^3