Calculus Easy 10 points?

Question

1. Find the most general solution of the differential equation ds/dt = 1/t^2 + cos t

A. s = -1/t^3 + sin t + c

B. s = -1/t + sin t + c

C. s = - 1/t - sin t + c

D. s = 3 / t^3 + sin t + c

2. Find the most general solution of the differential equation d^2 y / dx^2 = π

A. y = π/ 2 x^2 + Ax + A

B. y = π / 2 x^2 + Ax + B

C. y = πx^2 + Ax + B

D. y = πx^2 + Ax + A

3. Find the solution of the differential equation dy/dx = sin 3x; x = II/2, y =0

A. y = - 1/3 cos 3x

B. y = 1/3 (1 - cos 3x)

C. y = - 1/3 cos 3x + 1

D. y = -1/3 (1+ cos 3x)

 

 

Answer 1

1)

Apply integral on each side.

Apply the formulae

Option B is correct choice.

Answer 2

2)

Apply integral on each side.

Again apply integral on each side.

 

Apply the formulae

 

Option B is correct choice.

Answer 3

3)

Apply integral on each side.

Apply the formula

 

 

Substitute the C value in

Option A is correct choice.