Rajasthan Board RBSE Class 12 Maths Chapter 12 Differential Equation Ex 12.1
Find the order and degree of the following differential equations :
Question 1.
\(\frac { dy }{ dx } \) = sin 2x + cos 2x
Solution:
\(\frac { dy }{ dx } \) = sin 2x + cos 2x
The highest derivative of y = \(\frac { dy }{ dx } \) = (\(\frac { { d }^{ 1 }y }{ { dx }^{ 1 } } \))1
Thus, order = 1, degree = 1.
Question 2.
\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \) = sin x + cos x
Solution:
\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \) = sin x + cos x
The highest derivative of y = \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \) = (\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \))1
Thus, order = 2, degree = 1.
Question 3.
Solution:
The highest derivative of y =
Thus, order = 2, degree = 2.
Question 4.
Solution:
Question 5.
Solution:
Question 6.
xdx + ydy = 0
Solution:
x dx + y dy = 0
Thus, order = 1, degree = 1.
Question 7.
Solution:
Question 8.
Solution:
Thus, order = 1 degree = 2.