Differential Equations
Differential Equations
nta_pyq_2025_jan
Grade 12
Question:
If y = y(x) is the solution of the differential equation, 2 2 dy , then y (0) is equal to -1 x -1 x \pi -8 2 \sqrt4 - x 2 = ((sin ( )) - y) sin ( ), -2 \le x \le 2, y(2) = dx 2 2 4 6
Step-by-Step Solution
Key Concept: Apply the core result for formation and solution of differential equations and simplify using the given constraints.
(sin -1 x ) (sin -3 x ) 3 dy 2 2 (4) + y = dx \sqrt4 - x 2 \sqrt4 - x 2 3 2 -3 x 2 -1 x -1 x (sin ) (sin ) (sin ) 2 2 2 ye 2 = \int e 2 dx 2 4 - x 2 -1 x -(sin ) 2 x 2 -1 y = (sin ) - 2 + c ⋅ e 2 2 2 \pi y(2) = - 2 \Rightarrow c = 0 4 y(0) = -2 1 2x
Correct Answer: 4