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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)
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
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)
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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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)
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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