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