NCERT Class 12-Mathematics: Chapter – 9 Differential Equations Part 7 (For CBSE, ICSE, IAS, NET, NRA 2023)
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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: