Calculus Questions Solutions

AP calculus question. Help please! General and partial solutions.?

Solve the Bernoulli equation – (x) / 2 = x ^ 5. A) y = (-2 + Ce ^-x ^ 2) ^ (-1 / 4) b) y = (-1 + Ce ^-x ^ 2) ^ (-1 / 2) c) y = (-2 + Ce ^-x ^ 2) ^ (-1 / 2) d) none of these

y '- xy / 2 = x ^ 5 y' / y ^ 5 – ^ 4 = change X/2y x variables Ω = 1 / 4 ^ y '= Ω -4 / 5 y ^ y' the equation becomes in '+ Ω (2x) 4x =- Ω integration Use factor: exp (2 ∫ XDx) = exp (x ²) exp (x ²) * + exp' Ω (x ²) * (2x) =- Ω 4exp (x ²) * x ∫ (exp (x ²) * Ω) 'dx = -4 ∫ (exp (x ²) * x dx exp (x ²) Ω * =- 2exp (x ²) Ω = -2 + C C + / Exp (x ²) 1 / y ^ 4 = -2 C + / Exp (x ²) y = (-2 C & / exp (x ²))^(- quarter ) Election of a

AP / AB Calculus Test – Sample Questions 17 & 18