4.3.2 \(x^3+y'(x)=x \sqrt {x^4+4 y(x)}\)

ODE
\[ x^3+y'(x)=x \sqrt {x^4+4 y(x)} \] ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
Homogeneous equation, isobaric equation

Mathematica
cpu = 0.0737663 (sec), leaf count = 25

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

Maple
cpu = 0.072 (sec), leaf count = 47

\[ \left \{ {1 \left (\left (-{\it \_C1}+y \relax (x ) \right ) \sqrt {{x}^{4}+4\,y \relax (x ) }-{x}^{2} \left ({\it \_C1}+y \relax (x ) \right ) \right ) \left ({x}^{2}+\sqrt {{x}^{4}+4\,y \relax (x ) } \right ) ^{-1}}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x)+x^3 = x*(x^4+4*y(x))^(1/2), y(x),'implicit')

Maple raw output

((-_C1+y(x))*(x^4+4*y(x))^(1/2)-x^2*(_C1+y(x)))/(x^2+(x^4+4*y(x))^(1/2)) = 0