Question

The order and degree of the differential equation `((d^2y)/(dx^2))^2 + ((dy)/(dx))^2 = a^x` are ______ respectively.

विकल्प

• 1, 1

• 1, 2

• 2, 2

• 2, 1

Answer 1

The order and degree of the differential equation `((d^2y)/(dx^2))^2 + ((dy)/(dx))^2 = a^x` are 2, 2 respectively. 

Explanation:

Step 1: Determine the Order

• The order of a differential equation is the highest order derivative present.
• Here, the highest order derivative is `(d^2y)/(dx^2)`(Second derivative)
• So, the order is 2.

Step 2: Determine the Degree

• The degree of a differential equation is the power of the highest-order derivative after it is made free from radicals and fractions.
• Here, `(d^2y)/(dx^2)` is raised to the power of 2, which is already in polynomial form.
• So, the degree is also 2.