Question
In: Math
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
Solutions
milcah answered 2 years agoRelated Solutions
Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. dy dx...
Solve the given differential equation by using an appropriate
substitution. The DE is homogeneous.
dy
dx
=
y − x
y + x
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation...
Use the substitution x = et to transform the given
Cauchy-Euler equation to a differential equation with constant
coefficients. (Use yp for dy/dt and ypp for
d2y/dt2.)
x2y'' − 3xy' + 13y = 2 + 3x
Show the differential equation is not exact and by finding an appropriate integrating factor solve the...
Show the differential equation is not exact and by finding an
appropriate integrating factor solve the given initial problem.
(yx+y^2+ y) dx + (x+2y) dy =0
Use direct substitution to verify that y(t) is a solution of the given differential equation in...
Use direct substitution to verify that y(t) is a solution of the
given differential equation in Exercise Group 1.1.9.15–20. Then use
the initial conditions to determine the constants C or c1 and
c2.
17. y′′+4y=0, y(0)=1, y′(0)=0, y(t)=c1cos2t+c2sin2t
18. y′′−5y′+4y=0, y(0)=1 , y′(0)=0,
y(t)=c1et+c2e4t
19. y′′+4y′+13y=0, y(0)=1, y′(0)=0,
y(t)=c1e−2tcos3t+c2e−3tsin3t
27. The growth of a population of rabbits with unlimited
resources and space can be modeled by the exponential growth
equation, dP/dt=kP.
Write a differential equation to model a population of...
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...
a) Determine whether the given differential equation is exact. If it is exact, solve it. (If...
a) Determine whether the given differential equation is exact.
If it is exact, solve it. (If it is not exact, enter NOT.)
(2xy2 − 5) dx + (2x2y + 4) dy = 0
b) Solve the given differential equation by finding, as in
Example 4 of Section 2.4, an appropriate integrating factor.
(6 − 20y +
e−5x)
dx − 4 dy = 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.
(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
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
Solve the given differential equation by means of a power series about the given point x0....
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.
. y′′ − xy′ − y = 0, x0 = 1
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