1- Find the solution of the following equations. For each equation, 2- determine the type of...

1- Find the solution of the following equations. For each equation, 2- determine the type of the category that the equation belongs to. Separable equation, Homogenous equation, Linear equation, or Bernolli equation?

1. ydx − x ln xdy = 0

2. y ′ = (1+y^2) / (xy(1+x2))

3. xy′ + (1 + y^2 ) tan^−1 y = 0

4. y ′ = (y) / (x+ √xy)

5. y ′ = (y−x) / (y+x)

6. tan x dy/dx + y = 3x sec x

7. (2xy^5 − y)dx + 2xdy = 0

Expert Solution

milcah answered 2 years ago

Determine whether the equation is exact. If it is exact, find the solution. If it is...

Determine whether the equation is exact. If it is exact, find the solution. If it is not, enter NS. (8x^2−2xy+5)dx+(8y^2−x^2+8)dy=0

Find the Green's function for each of the following problem, and determine the solution of each...

Find the Green's function for each of the following problem, and determine the solution of each of the following boundary-value problem: y" + 4y = e^x y(0) = 0 y'(1) = 0

For each of the following differential equations, find the particular solution that satisfies the additional given...

For each of the following differential equations, find the particular solution that satisfies the additional given property (called an initial condition). y'y = x + 1

For each of the following equations, find the general solution: (x^2)y′′+xy′+ 4y= sin(lnx) + sin(2 lnx)...

For each of the following equations, find the general solution: (x^2)y′′+xy′+ 4y= sin(lnx) + sin(2 lnx) y′′+y=tcost Thank you!

Determine whether the equation is exact. If it is exact, FIND THE SOLUTION. If not write...

Determine whether the equation is exact. If it is exact, FIND THE SOLUTION. If not write NOT EXACT. A) (y/x + 12x) + (lnx - 3)y' = 0 x>0 Solve the given initial value problem. B) (12x2 + y − 1) − (14y − x)y' = 0, y(1) = 0 y(x) = Determine at least approximately where the solution is valid. (Enter your answer as an inequality for which the solution is valid when true.) The solution is valid as long as:...

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

1. Determine the form of a particular solution for the following differential equations. (Do not evaluate...

1. Determine the form of a particular solution for the following differential equations. (Do not evaluate the coefficients.) (a) y'' − y' − 6y = x^2 e^x sin x + (2x^3 − 1)e ^ cos x. (b) y'' − y' − 6y = (2 − 3x^3 )e^3x . (c) y'' + 4y' + 4y = x(e^x + e^−x )^2 . (d) y'' − 2y' + 2y = (x − 1)e^x sin x + x^2 e^−x cos x. 2. Find a...

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...

1)Find the power series solution for the equation y'' − y = x 2)Find the power...

1)Find the power series solution for the equation y'' − y = x 2)Find the power series solution for the equation y'' + (sinx)y = x; y(0) = 0; y'(0) = 1 Provide the recurrence relation for the coefficients and derive at least 3 non-zero terms of the solution.

Find the following system of equations find the equation of the phase trajectory, the phase velocity...

Find the following system of equations find the equation of the phase trajectory, the phase velocity and the fixed points: (Qualitative method) Also, sketch a few trajectories and show the directions of a point on the trajectories. My question is that what is the concept of drawing the trajectories no matter what it is a circle, ellipse or straight line

Question