4.428   y(x)y′(x) = ay(x )2 +b cos(c+ x)

ODE

y(x)y′(x) = ay(x)2 + bcos(c+ x)

ODE Classification

[_Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0723789 (sec), leaf count = 106

{{         ∘ ---------------------------------------}  {       ∘ ----------------------------------------}}
             (4a2 + 1)c1e2ax − 4abcos(c+ x)+ 2bsin(c+ x)           (4a2 + 1)c1e2ax − 4abcos(c+ x)+ 2bsin(c + x)
   y(x) → −-----------------√4a2-+-1----------------- ,  y(x) → -----------------√4a2-+-1-----------------

Maple
cpu = 0.036 (sec), leaf count = 51

{   2ax    2    2      2                 2ax                        2   }
 − 4e   -C1a + 4a (y(x)) + 4cos(x+ c)ab− e    C1 − 2sin(x+ c)b+ (y(x)) = 0

Mathematica raw input

DSolve[y[x]*y'[x] == b*Cos[c + x] + a*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -(Sqrt[(1 + 4*a^2)*E^(2*a*x)*C[1] - 4*a*b*Cos[c + x] + 2*b*Sin[c + x]]
/Sqrt[1 + 4*a^2])}, {y[x] -> Sqrt[(1 + 4*a^2)*E^(2*a*x)*C[1] - 4*a*b*Cos[c + x] 
+ 2*b*Sin[c + x]]/Sqrt[1 + 4*a^2]}}

Maple raw input

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

Maple raw output

-4*exp(2*a*x)*_C1*a^2+4*a^2*y(x)^2+4*cos(x+c)*a*b-exp(2*a*x)*_C1-2*sin(x+c)*b+y(
x)^2 = 0