Consider the differential equation dy/dx= e^x-1/2y. If y = 4 when x = 0 what is a value of y when x = 1?

A. √(e + 14)

Step-by-step explanation:

separating the variables, we have

2ydy = ( - 1)dx

integrating, we have

∫ydy = ∫( - 1)dx

∫ydy = ∫dx - ∫1dx + C

2y²/2 = - x + C

y² = - x + C

when x = 0, y = 4

So,

y² = - x + C

4² = - 0 + C

16 = 1 + C

16 = 1 + C

C = 16 - 1

C = 15

So,

y² = - x + 15

when x = 1, we find y

y² = - 1 + 15

y² = e + 14

y = √(e + 14)

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step-by-step explanation: