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$$c) 3e^{6}$$c)3e6

The given differential equation is a first order linear homogeneous differential equation. We can solve it by separating variables and integrating.

  1. Rewrite the differential equation as:

$$f'(x)=-2f(x)$$f′(x)=−2f(x)
2. Separate the variables:

$$\frac{df}{f}=-2dx$$fdf​=−2dx
3. Integrate both sides:

$$\int \frac{df}{f} =-2\int dx$$∫fdf​=−2∫dx

STEP1

STEP2

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$$c) 3e^{6}$$c)3e6

The given differential equation is a first order linear homogeneous differential equation. We can solve it by separating variables and integrating.

  1. Rewrite the differential equation as:

$$f'(x)=-2f(x)$$f′(x)=−2f(x)
2. Separate the variables:

$$\frac{df}{f}=-2dx$$fdf​=−2dx
3. Integrate both sides:

$$\int \frac{df}{f} =-2\int dx$$∫fdf​=−2∫dx

Explanation

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$$c) 3e^{6}$$c)3e6

The given differential equation is a first order linear homogeneous differential equation. We can solve it by separating variables and integrating.

  1. Rewrite the differential equation as:

$$f'(x)=-2f(x)$$f′(x)=−2f(x)
2. Separate the variables:

$$\frac{df}{f}=-2dx$$fdf​=−2dx
3. Integrate both sides:

$$\int \frac{df}{f} =-2\int dx$$∫fdf​=−2∫dx

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