4.1.10 \(y'(x)=x^2 \left (a x^3+b y(x)\right )\)

ODE
\[ y'(x)=x^2 \left (a x^3+b y(x)\right ) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0103166 (sec), leaf count = 32

\[\left \{\left \{y(x)\to c_1 e^{\frac {b x^3}{3}}-\frac {a \left (b x^3+3\right )}{b^2}\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 29

\[ \left \{ y \relax (x ) =-{\frac {a{x}^{3}}{b}}-3\,{\frac {a}{{b}^{2}}}+{{\rm e}^{{\frac {b{x}^{3}}{3}}}}{\it \_C1} \right \} \] Mathematica raw input

DSolve[y'[x] == x^2*(a*x^3 + b*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> -((a*(3 + b*x^3))/b^2) + E^((b*x^3)/3)*C[1]}}

Maple raw input

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

Maple raw output

y(x) = -1/b*x^3*a-3/b^2*a+exp(1/3*b*x^3)*_C1