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Chinmayee Patra posted an Question
May 01, 2021 • 16:34 pm
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30 points
30 points
- IIT JAM
- Mathematics (MA)
1. let a, b, k > 0. slove the initial value problem -ay + by' = 0, y0) =k also show that (a) if k , then the solution y(x) is monotonically increasing on (0, co
1. Let A, B, k > 0. Slove the initial value problem -Ay + By' = 0, y0) =k Also show that (a) if k , then the solution y(x) is monotonically increasing on (0, co) and tends to Jas x00. (b)(a) if k >> then the solution y(x) is monotonically decreasing on (0, co) and tends to as xoo 2. Show that the solution y(t) of the initial value problem y' = 1 +y +y* cost, y0) = 0 exists on the interval t E [0,1/3] 3. Show that every solution of the equation+ a(t)y = f(t)with a(t) and f() continuous for -0t< o, a(t) 2 c> 0 and lim-f() = 0, tends to zero as t approches infinity.
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