MTH 286 Quiz: MTH 286 Cleveland State Quiz2s03sol
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, y(0) = 0 (a) find a formula for the solution. Solution: the di erential equation is separable, so we have (cid:1) (y + 2)dy = (cid:1) + 2y = ln|t 1| + c y2. + 2y ln|t 1| c = 0. From the initial condition, y = 2 (cid:2)4 4(1/2)( ln|t 1| c) = 2 (cid:2)4 + 2 ln|t 1| + 2c. y(0) = 0. = 2 (cid:2)4 + 2 ln|0 1| + 2c. Therefore c = 0, and the solution must be the positive square root, so y(t) = 2 +(cid:2)4 + 2 ln|t 1|. (b) state the domain of de nition of the solution. Solution: the argument of the square root must always be positive, so. 4 + 2 ln|t 1| 0. 2 ln|t 1| 4 ln|t 1| 2. |t 1| e 2. t 1 e 2 or 1 t e 2.
