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