GATE EE 2020 Set 1 — Question 26
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Engineering Mathematics → Differential Equations → First-Order Equations
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Question
Consider the initial value problem below. The value of at , (rounded off to decimal places) is ________.
Correct answer
0.8774 to 0.8952
Solution
The given differential equation is a first-order linear ODE:This is in the standard form , where and .
The integrating factor is:The general solution is given by:Using integration by parts for :Applying the initial condition :Thus, the particular solution is:At :Rounding to 3 decimal places, we get .
The integrating factor is:The general solution is given by:Using integration by parts for :Applying the initial condition :Thus, the particular solution is:At :Rounding to 3 decimal places, we get .
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