The number of arbitrary constants in the particular solution of a differential equation of third order are _____

Question

The order and the degree of the differential equation \[ \sqrt{1 + \left(\frac{d^2y}{dx^2}\right)^2} = \sqrt{x + \left(\frac{dy}{dx}\right)^6} \] are respectively _____ and _____

Answer 1

Step 1: Understanding the Concept:
A General Solution contains arbitrary constants ($C_1, C_2$, etc.). A Particular Solution is obtained by giving specific values to these constants based on initial conditions.
Step 2: Formula Derivation:
Number of constants in General Solution = Order of Equation. Number of constants in Particular Solution = 0.
Step 3: Explanation:
Since a particular solution is a specific case where the constants have already been solved for, there are no "arbitrary" constants left in the expression.
Step 4: Final Answer:
The number of arbitrary constants is 0.

The number of arbitrary constants in the particular solution of a differential equation of third order are _____

Show Hint

The Correct Option is D

Solution and Explanation

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