Question

Find the fundamental solution to the following differential equation.

y''+y'-2y=0, t_{0}=0

Answer #1

a) Find the general solution of the differential equation
y''-2y'+y=0
b) Use the method of variation of parameters to find the general
solution of the differential equation y''-2y'+y=2e^t/t^3

Consider the differential equation x^2y′′ − 3xy′ − 5y = 0. Note
that this is not a constant coefficient differential equation, but
it is linear. The theory of linear differential equations states
that the dimension of the space of all homogeneous solutions equals
the order of the differential equation, so that a fundamental
solution set for this equation should have two linearly fundamental
solutions.
• Assume that y = x^r is a solution. Find the resulting
characteristic equation for r....

Find a particular solution for the differential equation by
variation of parameters.
y''- y' -2y = e^3x , y(0) = -3/4 , y'(0)=15/4

Differential Equations problem
If y1= e^-x is a solution of the differential equation
y'''-y''+2y=0 . What is the general solution of the differential
equation?

Find the general solution to the differential equation
2y'+y=3x

Find the particular solution of the differential equation: y "+ 2y
'+ y = 3x + 5 + 4e^-x

Find the general solution of the given differential
equation.
y'' − y' − 2y = −8t + 6t2
y(t) =

find the general solution of the differential equation:
y''+2y'+4y=xcos3x

Find the solution of the Differential Equation
X^2y''-xy'+y=x

Given the differential equation to the right y''-3y'+2y=0
a) State the auxiliary equation.
b) State the general solution.
c) Find the solution given the following initial conditions
y(0)=4 and y'(0)=5

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