## Rajasthan Board RBSE Class 12 Maths Chapter 12 Differential Equation Miscellaneous Exercise

Question 1.

Solution of differential equation

Solution:

Hence, option (b) is correct.

Question 2.

Solution:

Thus Option (a) is correct.

Question 3.

Solution of \(\frac { dy }{ dx } \) + cos x tan y = 0 is :

(a) log sin y + sin x + C

(b) log sin x sin y = C

(c) sin y + log sin x + C

(d) sin x sin y + C

Solution:

Hence, option (a) is correct.

Question 4.

Solution:

Thus Option (b) is correct.

Question 5.

Solution:

Thus Option (a) is correct.

Question 6.

Solution:

Thus Option (b) is correct.

Question 7.

Solution \(\frac { dy }{ dx } \) = cos^{2} y is :

(a) x + tan y = C

(b) tan y = x + C

(c) sin y + x = C

(d) sin y – x = C

Solution:

Thus Option (b) is correct.

Question 8.

Solution:

Thus Option (d) is correct.

Question 9.

By which displacement the differenting equation

will be correct into linear equation :

(a) y = 1

(b) y^{2} = t

(c) \(\frac { 1 }{ y } \) = t

(d) \(\frac { 1 }{ { y }^{ 2 } } \) = t

Solution:

Hence, option (c) is correct.

Question 10.

By which displacement the differential equation

will be correct into linear equation :

(a) \(\frac { 1 }{ y } \) = v

(b) y^{-2} = v

(c) y^{-3} = v

(d) y^{3} = v

Solution:

Hence, option (b) is correct.

Question 11.

Find the general solution of differential equation

Solution:

This is required solution

Question 12.

Find the integrating factor of differential equation \(\frac { dy }{ dx } \) + y tan x = sin x.

Solution:

Question 13.

Find the integrating factor of differential equation

Solution:

Question 14.

Write the form of differential equation dy cos (x + y) \(\frac { dx }{ dx } \) = 1.

Solution:

Given equation is of the form of converting variables separately.

Question 15.

Write the form of differential function

Solution:

Linear equation

Question 16.

Write the general solution of the following differential equation

Solution:

Similar Question

If we take equation

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution: