4.7.48 \(x^3 y'(x)=x^4+y(x)^2\)

ODE
\[ x^3 y'(x)=x^4+y(x)^2 \] ODE Classification

[[_homogeneous, `class G`], _rational, _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.0201781 (sec), leaf count = 22

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

Maple
cpu = 0.014 (sec), leaf count = 24

\[ \left \{ \ln \relax (x ) -{\it \_C1}-{\frac {{x}^{2}}{{x}^{2}-y \relax (x ) }}=0 \right \} \] Mathematica raw input

DSolve[x^3*y'[x] == x^4 + y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> (x^2*(-1 + C[1] + Log[x]))/(C[1] + Log[x])}}

Maple raw input

dsolve(x^3*diff(y(x),x) = x^4+y(x)^2, y(x),'implicit')

Maple raw output

ln(x)-_C1-x^2/(x^2-y(x)) = 0