VARIABLE SEPARABLE DIFFERENTIAL EQUATION WORKSHEET

Problem 1 :

If F is the constant force generated by the motor of an automobile of mass M , its velocity V is given by

where k is a constant. Express V in terms of t given that V = 0 when t = 0.

Solution

Problem 2 :

The velocity v , of a parachute falling vertically satisfies the equation

where g and k are constants. If v and x are both initially zero, find v in terms of x .

Solution

Problem 3 :

Find the equation of the curve whose slope is

(y - 1)/(x² + x)

and which passes through the point (1, 0).

Solution

Problem 4 :

Solve 

Solution

Problem 5 :

Solve 

Solution

Problem 6 :

Solve 

Solution

Problem 7 :

Solve

Solution

Problem 8 :

Solve

Solution

Problem 9 :

Solve

(y dx - x dy) cot (x/y) = ny² dx.

Solution

Problem 10 :

Solve 

Solution

Problem 11 :

Solve

Solution

Problem 12 :

Solve

Solution

Problem 12 :

Solve

Solution