In: Advanced Math

y"+y'-6y=1

1. general solution of corresponding homogenous equation

2. particular solution

3.solution of initial value problem with initial conditions y(0)=y'(0)=0

y"-2y'+y=cos2t
1. general solution of corresponding homongenous equation
2. particular solution
3.solution of initial value problem with initial conditions
y(0)=y'(0)=0

y"+y=cos(9t/10)
1. general solution of corresponding homongenous equation
2. particular solution
3.solution of initial value problem with initial conditions
y(0)=y'(0)=0
4. sketch solution in part 3

Find a particular solution to the following non homogenous
equations
1) y''' + y = t^3 + sin (t) + 11e^t
2) y'' + y = 2tsin(t)
3) y''''' - 4 y''' = e^2t + t^2 +5t + 4

Find the general solution for differential equation
x^3y'''-(3x^2)y''+6xy'-6y=0, y(1)=2, y'(1)=1,
y''(1)=-4

1)Find the general solution of the given second-order
differential equation.
y'' − 7y' + 6y = 0
2)Solve the given differential equation by undetermined
coefficients.
y'' + 4y = 6 sin(2x)

Find a particular solution to
y''+6y'+9y=(-18.5e^(-3t))/(t^2+1)

1) . Solve the IVP:
y^''+6y^'+5y=0, y(0)=1, y^' (0)=3
2. Find the general solution to each of the following:
a) y^''+2y^'+5y=e^2x
b) y^''+2x/(x^2+1) y'=x
c) y^''+4y=1/(sin(2x)) (use variation of parameters)

1. solve the initial value problem.
(t^(2)+1)y'+2ty=tant , y(0)=2
2.find the solution to this initial value problem.
yy'=e^x+x , y(0)=y_0
y_0 is a nonzero constant.

Find the general solution to the following equation:
y''' + 3y''−4y'−6y = cos(t)

Find the general solution to the differential equation below.
y′′ − 6y′ + 9y = 24t−5e3
Calculate the inverse Laplace transform of ((3s-2)
e^(-5s))/(s^2+4s+53)
Calculate the Laplace transform of y = cosh(at) using the
integral definition of the Laplace transform. Be sure to note any
restrictionson the domain of s. Recall that cosh(t)
=(e^t+e^(-t))/2

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