GATE CE 2025 Set 1 — Question 47
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Engineering Mathematics → Ordinary Differential Equations → Higher-Order Linear ODEs
Last updated
Question
Let be the solution of the initial value problem , where and . Then, is equal to ______________________ (rounded off to 1 decimal place).
Correct answer
5.7 to 5.9
Solution
The characteristic equation is .
(repeated root).
The general solution is .
Using initial conditions:
.
.
.
So, .
At :
.
Rounding to 1 decimal place, .
(repeated root).
The general solution is .
Using initial conditions:
.
.
.
So, .
At :
.
Rounding to 1 decimal place, .
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