NCERT Class 12-Mathematics: Chapter –9 Differential Equations Part 7

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Question 11:

If is a solution of and , then find the value of

Answer:

Given that,

On integrating both sides, we get

When then

On putting in Eq. (i), we get

Question 12:

If is a solution of then show that

Answer:

Given that,

Dividing both sides by

Which is a linear differential equation.

On comparing it with we get

The complete solution is

The general solution is

When

Question 13:

Form the differential equation having , where A and B are arbitrary constants, as its general solution.

Answer:

Question 14:

Form the differential equation of all circles which pass through origin and whose centres lie on axis.

Answer:

Question 15:

Find the equation of a curve passing through origin and satisfying the differential equation

Answer:

Question 16:

Solve:

Answer: