Final answer to the problem
$x=\frac{3\left(2\cos\left(2f\right)+\frac{11}{6}\sin\left(2f\right)\right)}{-8}$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation (d^2x)/(df^2)+2dx/df5x=12cos(2f)+3sin(2f). Combining like terms \frac{d^2x}{df^2} and 5x. Divide all the terms of the differential equation by 2. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(f)=3 and Q(f)=\frac{12\cos\left(2f\right)+3\sin\left(2f\right)}{2}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Final answer to the problem
$x=\frac{3\left(2\cos\left(2f\right)+\frac{11}{6}\sin\left(2f\right)\right)}{-8}$
