Final answer to the problem
$\frac{1}{e^{5f}g}=\frac{1}{e^{3f}}+C_0$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Grouping the terms of the differential equation
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$\frac{dg}{df}+5g=3e^{2f}g^2$
Learn how to solve problems step by step online. Solve the differential equation dg/df=3e^(2f)g^2-5g. Grouping the terms of the differential equation. We identify that the differential equation \frac{dg}{df}+5g=3e^{2f}g^2 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 2. Simplify.
Final answer to the problem
$\frac{1}{e^{5f}g}=\frac{1}{e^{3f}}+C_0$
