4.1.43 \(y'(x)=(y(x)+x)^2\)

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

[[_homogeneous, `class C`], _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.00951565 (sec), leaf count = 30

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

Maple
cpu = 0.047 (sec), leaf count = 15

\[ \left \{ -\arctan \left (x+y \relax (x ) \right ) +x-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y'[x] == (x + y[x])^2,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

-arctan(x+y(x))+x-_C1 = 0