Question
In: Advanced Math
5. Solve the following differential equation using the given initial conditions (Use convolution and set up the...
5. Solve the following differential equation using the given initial conditions (Use convolution and set up the integral but do not integrate.)
y'’ − 2y’ + 2y = 18e−t sin3t; y(0) = 0, y’(0) = 3
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1,...
Solve the differential equation by variation of parameters,
subject to the initial conditions
y(0) = 1, y'(0) = 0.
y'' + 2y' − 8y = 4e−3x − e−x
Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1,...
Solve the differential equation by variation of parameters,
subject to the initial conditions
y(0) = 1, y'(0) = 0.
2y'' + y' − y = x + 7
1. Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for...
1.
Set-up the appropriate differential equation(s) and solve to
derive the general equation of motion for a human sized “dummy”
moving vertically (up/down) under the following assumptions:
(a)The initial elevation is h0 ft.
(b)The initial velocity is V0 ft./sec.
(c)All motion vertical (ignore any sideways motion).
(d)The force due to wind is proportional to velocity and in the
opposite
direction of velocity.
(e)The “terminal velocity” is 120mph (e.g. lim
t→∞ (V)= 120 mph).
(f)Force = Mass * Acceleration.
(g)Acceleration due to...
Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A....
Solve the given differential equation using an appropriate
substitution. The DE is a Bernoulli equation,
A. dy/dx = y(xy^6 - 1)
B. x dy/dx + y = 1/y^2
C. t^2 dy/dt + y^2 = ty
Solve Legendre’s equation for the given initial conditions. (1 — х)у -
Solve Legendre’s equation for the given initial conditions. (1 - x2)y - 2xy + 6y = 0
Solve the differential equation y'' − y' − 2y = 9e^2t , with initial conditions y(0)...
Solve the differential equation y'' − y' − 2y = 9e^2t , with
initial conditions y(0) = 3, y' (0) = −2, using two different
methods. Indicate clearly which methods you are using. First
method:
Second method:
Solve the following equation using Green’s functions. Set up the integral for the particular solution and...
Solve the following equation using Green’s functions. Set up the
integral for the particular solution and evaluate
y''+9y=x+sinx y(0)=1,y'(0)=2
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independent solutions (unless the series terminates sooner). If
possible, find the general term in each solution.
(1-x)y"+xy-y=0, x0=0
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independent solutions (unless the series terminates sooner). If
possible, find the general term in each solution.
(4-x2)y"+2y=0, x0
Use the Euler method to solve the following differential equation for the domain [2,2.5]. Use the...
Use the Euler method to solve the following differential
equation for the domain [2,2.5]. Use the step-size ℎ = 0.1.
?′=?ln?/? ;?(2)=?1
b) Use the third order Taylor series method to find ?(0.1) and
?(0.2),
where ?′=1+2?? ;?(0)=0. Use the step-size ℎ=0.1.
c) Solve the problem in part (ii) using the fourth order Runge –
Kutta method.
d) Solve the problem in part (ii) using the Predictor – Corrector
method.
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