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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.

- Rewrite the differential equation as:
$$f'(x)=-2f(x)$$f′(x)\=−2f(x)
- Separate the variables:
$$\\frac{df}{f}=-2dx$$fdf​\=−2dx
- Integrate both sides:
$$\\int \\frac{df}{f} =-2\\int dx$$∫fdf​\=−2∫dx

STEP 1

STEP 2

Gauth AI

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

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

- Rewrite the differential equation as:
$$f'(x)=-2f(x)$$f′(x)\=−2f(x)
- Separate the variables:
$$\\frac{df}{f}=-2dx$$fdf​\=−2dx
- Integrate both sides:
$$\\int \\frac{df}{f} =-2\\int dx$$∫fdf​\=−2∫dx

Explanation

12

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Gauth AI

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

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

- Rewrite the differential equation as:
$$f'(x)=-2f(x)$$f′(x)\=−2f(x)
- Separate the variables:
$$\\frac{df}{f}=-2dx$$fdf​\=−2dx
- Integrate both sides:
$$\\int \\frac{df}{f} =-2\\int dx$$∫fdf​\=−2∫dx

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