Explain the basic concepts ordinary and partial 2 differential equations (ODEs,PDEs), order general and particular solutions...

Explain the basic concepts ordinary and partial 2 differential equations (ODEs,PDEs), order general and particular solutions initial value problems (IVPs)Give examples ?

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Colby Messinger answered 2 years ago

Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b)...

Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b) use it to find the solution satisfying the given initial data. Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u u(x, x) = e −x 2 Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y u(0, y) = 1 + y 2 Exercise 3. y ∂u ∂x + x ∂u ∂y = 0 u(x, 0) = x 4 Exercise 4. ∂u...

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

Find the General Solutions to the given differential equations y(t) = a) 6y' +y = 7t^2...

Find the General Solutions to the given differential equations y(t) = a) 6y' +y = 7t^2 b) ty' − y = 9t2e−9t, t > 0 c) y' − 8y = 9et d) y' + y/t = 6 cos 5t, t > 0

Find the general solution of the following differential equations (complementary function + particular solution). Find the...

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection or by (6.18), (6.23), or (6.24). Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form [see (6.26) and the discussion after (6.15)]. (D2+2D+17)y = 60e−4x sin 5x

Solve the following first order differential equations: (a) 2/?^ ???/?? = 4?^2? ; ?(0) = −1/...

Solve the following first order differential equations: (a) 2/?^ ???/?? = 4?^2? ; ?(0) = −1/ 3 (b) ??/?? + ? = ? ; ?(0) = 5 (c) ??/?? + ? /? = ? 3 ; ? ( 1/2 ) = 1

Find the particular integral of the following differential equations.(Explain each step clearly) (a) d2y/dx2 + y...

Find the particular integral of the following differential equations.(Explain each step clearly) (a) d2y/dx2 + y = (x + 1) sin x. show that the answer is yp(x) = − 1/8 [ (2x2 + 4x − 1) cos x − (2x + 2) sin x ] (Hint:In this case, we substitute sin αx or cos αx with eiαx then use the shift operator. In the case of sin αx we extract the imaginary part.)

Determine the solution of a homogeneous linear first order Ordinary Differential Equation system: (use 2 methods,...

Determine the solution of a homogeneous linear first order Ordinary Differential Equation system: (use 2 methods, substitution method, and matrix method) x1' = - 4x1-6x2 x2' = x1+ x2 With the initial values: x1 (0) = 2 ; x2 (0) = -1 b. x1' = -x2 x2' = -x1 With initial values: x1 (0) = 3 ; x2 (0) = 1

2- Ordinary Differential Equations a) y'+y = sen(x) b)By what technique do you solve an ODE...

2- Ordinary Differential Equations a) y'+y = sen(x) b)By what technique do you solve an ODE below: (x + yˆ2) dy + (y-xˆ2) dx = 0? c) Solve the following ODE by Exact Equation: y '= 2x d) Resolution y '= (2 + exp (xy)) / (2y-xexp (xy))

1. Evaluate the general solutions of the following differential equations: (A) y''+y= 1/cos(x) (B) y'''-y''= -3x+1...

1. Evaluate the general solutions of the following differential equations: (A) y''+y= 1/cos(x) (B) y'''-y''= -3x+1 (C) 2(y')^2= y''(y-1)

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Explain the basic concepts ordinary and partial 2 differential equations (ODEs,PDEs), order general and particular solutions...

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