91Ó°ÊÓ

Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of undetermined coefficients. $$ y^{\prime \prime}-5 y^{\prime}+6 y=2 e^{t} $$

In each of Problems 1 through 12 find the general solution of the given differential equation. $$ y^{\prime \prime}-2 y^{\prime}-3 y=3 e^{2 x} $$

find the Wronskian of the given pair of functions. $$ e^{2 t}, \quad e^{-3 t / 2} $$

In each of Problems 1 through 10 find the general solution of the given differential equation. \(y^{\prime \prime}-2 y^{\prime}+y=0\)

In each of Problems I through 8 find the general solution of the given differential equation. $$ y^{\prime \prime}+2 y^{\prime}-3 y=0 $$

In each of Problems 1 through 8 determine whether the given pair of functions is linearly independent or linearly dependent. \(f(t)=t^{2}+5 t, \quad g(t)=t^{2}-5 t\)

Write the given expression as a product of two trigonometric functions of different frequencies. \(\cos 9 t-\cos 7 t\)

use Euler’s formula to write the given expression in the form a + ib. $$ \exp (1+2 i) $$

determine \(\omega_{0}, R,\) and \(\delta\) so as to write the given expression in the form \(u=R \cos \left(\omega_{0} t-\delta\right)\) $$ u=3 \cos 2 t+4 \sin 2 t $$

In each of Problems 1 through 8 determine whether the given pair of functions is linearly independent or linearly dependent. \(f(\theta)=\cos 3 \theta\) \(\quad\) \(g(\theta)=4 \cos ^{3} \theta-3 \cos \theta\)