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 = 0.17626 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {x^4+4 c_1}{4 \left (x^5+x^3\right )}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 22
\[\left [y \left (x \right ) = \frac {\frac {x^{4}}{4}+\textit {\_C1}}{x^{3} \left (x^{2}+1\right )}\right ]\] 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))
Maple raw output
[y(x) = (1/4*x^4+_C1)/x^3/(x^2+1)]