JEE Main 2018 — Differential Equations Question with Solution
From: JEE Main 2018 (Online) 15th April Morning Slot
Question
Let y = y(x) be the solution of the differential equation
where f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right.
If y(0) = 0, then is :
where f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right.
If y(0) = 0, then is :
Choose an option
Show full solutionCorrect option: D
Correct answer
D
Step-by-step explanation
When x [0, 1], then + 2y = 1
y = + C1e2x
y(0) = 0 y(x) = e2x
Here, y(1) = e2 =
When , then + 2y = 0 y = c2 e2x
y(1) = = c2e2 C2 =
y(x) =
y = + C1e2x
y(0) = 0 y(x) = e2x
Here, y(1) = e2 =
When , then + 2y = 0 y = c2 e2x
y(1) = = c2e2 C2 =
y(x) =
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This is a previous-year question from JEE Main 2018, covering the Differential Equations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.