Consider the differential equation 16y" + y = sec(x/4) tan(x/4) Find the general solution of the...
Question:
Consider the differential equation:
{eq}16'' + y = sec(\frac{x}{4}) tan(\frac{x}{4}) {/eq}
Find the general solution of the related homogeneous differential equation. Find the general solution of the nonhomogeneous differential equation.
General Solution:
We have to find the general solution of the second-order differential equation.
For finding the general solution of the equation of the form {eq}ay''+by'+cy=g(x) {/eq}, first, we calculate the general solution of the homogenous equation and then we calculate the particular solution of the non-homogeneous equation and lastly we combine both the results.
Answer and Explanation: 1
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Given
{eq}16y'' + y = sec(\frac{x}{4}) tan(\frac{x}{4}) \\ y''+\dfrac{1}{16}y''=\dfrac{1}{16}sec(\frac{x}{4}) tan(\frac{x}{4}) {/eq}
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