Question

DADA A EQUAÇÃO DIFERENCIAL F''(X)=4X-1 DETERMINE A SOLUÇÃO F(X) CONFORME CONDIÇOES AUXILIARES F'(2)=2 E F(1)=3 PROPOSTAS

Answer 1

$f''(x)=4x-1\\\\ f'(x)=\int f''(x) \\\\ f'(x)= \int(4x-1)\\\\f'(x)= \frac{4x^2}{2}-x +C\\\\\boxed{f'(x)=2x^2-x+C} \\\\\text{como f'(2)=2}\\\\ f'(2)=2*(2)^2-2+C=2\\\\ 8-2+C=2\\\\C= -4\\\\\boxed{\boxed{f'(x)=2x^2-x-4}}\\\\\\\\\\ f(x)=\int f'(x)\\\\f(x)=\int (2x^2-x-4)\\\\\boxed{f(x)= \frac{2x^3}{3}- \frac{x^2}{2}-4x+C} \\\\ \text{como f(1)=3}\\\\ \frac{2}{3}- \frac{1}{2}-4+C=3 \\\\ \frac{2*2-1*3}{3*2}+C=3+4 \\\\ \frac{1}{6}+C=7\\\\C=7- \frac{1}{6}\\\\C= \frac{41}{6}$


$\boxed{\boxed{f(x)=\frac{2x^3}{3}- \frac{x^2}{2}-4x+ \frac{41}{6} }}$

Answer 2

Resposta:

$f(x)=2/3x^3-1/2x^2-4x+41/6$

Explicação passo-a-passo:

Conferido no AVA.