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y(x) = x-3/2 is a solution to 4x2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64
Solution: As we noticed in previous illustration the function is a solution and we can after that notice that:
And therefore this solution also meets the initial conditions of y (4) = 1/8 , and y'(4) = -3/64.
Actually, y (x) = x-3/2 is the merely solution to this differential equation which satisfies such two initial conditions.
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Determine an actual explicit solution to y′ = t/y; y(2) = -1. Solution : We already identify by the previous illustration that an implicit solution to this IVP is y 2 = t 2 -
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