Differential equations of the form are called separable. Such equations can often be solved by direct integration. Suppose that f and y have anti-derivatives given by F and G, i.e. Then the solution...

Differential equations of the form

are called separable. Such equations can often be solved by direct integration. Suppose that f and y have anti-derivatives given by F and G, i.e.

Then the solution of (2.62) satisfies

where c is a constant that has to be determined using the initial condition

(a)    Consider

Use the method above to solve this problem. Verify your answer by checking that both conditions in (2.66) hold.

(b)   Consider

Use the method above to solve (2.67). Verify that the solutions provided in Examples 2.4 and 2.5 are correct.

(c)    Consider

Use the method above to solve this problem. Verify your answer by checking that both conditions in (2.68) hold.