Find f. f double prime (theta) = sin theta + cos theta, f(0) = 3, f prime (0) = 4.
Question:
Find {eq}f {/eq}.
{eq}{f}''(\theta) = \sin \theta + \cos \theta, \; f(0) = 3, \; {f}' (0) = 4 {/eq}
Solving Nonhomogeneous Equations Using Undetermined Coefficients:
If we have an initial value problem in the form
{eq}f(D)y = R(x) {/eq}
where {eq}f(D) {/eq} is a differential polynomial, we can find a particular solution {eq}y_p {/eq} by solving the auxiliary equation {eq}g(m) = 0 {/eq}, where g is a polynomial such that
{eq}g(D)R = 0 {/eq}
Our general solution will then be in the form
{eq}y = y_c + y_p {/eq}
where {eq}y_c {/eq} is obtained by solving the auxiliary equation
{eq}f(m) = 0. {/eq}
Answer and Explanation:
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View this answerFor the initial value problem
{eq}{f}''(\theta) = \sin \theta + \cos \theta, \; f(0) = 3, \; {f}' (0) = 4 {/eq},
the auxiliary equation to the...
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Chapter 10 / Lesson 15The method of undetermined coefficients is used to solve a class of nonhomogeneous second order differential equations. This method makes use of the characteristic equation of the corresponding homogeneous differential equation.
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