Problem

Find the general form of f if f′(x)=4f(x).

Answer

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Answer

So, the general form of the function f(x) is f(x)=Ce4x.

Steps

Step 1 ：The given function is f′(x)=4f(x). This is a first order linear differential equation.

Step 2 ：The general solution of this type of differential equation is given by f(x)=Ce4x, where C is a constant.

Step 3 ：So, the general form of the function f(x) is f(x)=Ce4x.

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