Question

a soluçao da equaçao diferencial dy/dx =4(x^2 + 1), com y(0)=0 e:

Answer 1

$f(x) = 4( {x}^{2} + 1) \\ f'(x) = 4(2x + 0) \\ f'(x) = 8x \\ \\ f'(0) = 8 \times 0 = 0$

Answer 2

Resposta:

dy/dx =4(x^2 + 1)

∫dy =4 ∫  (x^2 + 1) dx

y=4 *(x³/3+x) + c

Sabemos que y(0) =0

0 =4*(0³/3+0)+ c   ==>c=0

Solução :

y =(4/3)*x³ + x