# RBSE Solutions for Class 12 Maths Chapter 12 Differential Equation Miscellaneous Exercise

## 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 $$\frac { dy }{ dx }$$ = cos2 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) y2 = 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) y3 = 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: