Find the solution of the separable equations a) the general solution: displaystyle dy/dt = t/[y^2] b) the unique solution to: dy/dt = 1/y such that if x = 3 then y = 1.

(a) The general solution of given differential equation is .

(b) The unique solution is .

Step-by-step explanation:

(a)

The given differential equation is

Use variable separable method, to solve the above differential equation.

Separate the variables.

Integrate both sides.

The general solution of given differential equation is .

(b)

The given differential equation is

Use variable separable method, to solve the above differential equation.

Separate the variables.

Integrate both sides.

           ... (1)

It is given that y=1 at t=3. Substitute y=1 and t=3 in the above equation.

Substitute in equation (1).

Therefore the unique solution is .

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)