Differential Equations
Formation of Differential Equations
IIT-JEE 2005
Grade 12
Question:
The differential equation representing the family of curves $y = Ae^{2x} + Be^{-2x}$ (where $A, B$ are arbitrary constants) is:
(1) $\frac{d^2y}{dx^2} = 4y$
(2) $\frac{d^2y}{dx^2} = 2y$
(3) $\frac{d^2y}{dx^2} + 4y = 0$
(4) $\frac{d^2y}{dx^2} = -4y$
Step-by-Step Solution
Key Concept: Differentiate the relation twice with respect to $x$ and eliminate the two arbitrary constants $A$ and $B$ between the original relation and its derivatives.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)