8.) Match the following differential equations with their phase portraits A.) x" + 10x' + 24x = 0 B.) x" + 2x = 0 C.) x" - 2x' - 3x = 0 D.) x" 4x' + 12x = 0

Q: The path travelled by a long period comet as it passes near the sun is described by a hyperbola.…

A: Given:- The path travelled by a long period comet as it passes near the sun is described by a…

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: Given

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y=ae +be¯ª.

A:

Q: Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e-*. (a) Verify that yp = -3x +…

A:

Q: Consider the following autonomous first-order differential equation. y' = y² + 2y which of the…

A:

Q: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

A:

Q: The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and…

A: Given that        y''+y'2+4=0‐‐‐‐1        we have to solve this using the substitution        u=y'

Q: Assume that the rate of change of y is proportional to y. Solve the resulting differential equation…

A:

Q: Find the differential equation of the cubics : cy^2= x^2 ( x - a ) with a held fixed.

A: Here c is arbitrary constant and a  is fixed. So we have to find a differential equation which does…

Q: Q-1. Form the second-order differential equation using the parametric definition of y = asin0, x Y =…

A:

Q: What is the order of the lowest order homogeneous differential equation which has a particular…

A:

Q: Obtain the general solution of the given differential equation: tanydy = sin3xdx

A: The given differential equations tan2y dy=sin3x dx⇒sec2y-1 dy=143sinx-sin3x dx    As…

Q: 4. Find a third-order linear homogeneous differential equation which has the function r(t) = 3e-t +…

A:

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: 1. State the order of the given ordinary differential equation. Determine whether the equation is…

A: Given: sinθy''' -cosθy' = 2 To state: The order of the given differential equation and to determine…

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A:

Q: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

A:

Q: Determine the general solution and the particular curve that goes through point (0,0) of the e* cos…

A:

Q: Form a differential equation from the given function. y = Asin(2x)-5cos(2x)

A: Giveny=Asin(2x)-5cos(2x)   ----{1}

Q: A solution for the differential equation is y = eux A1 sin (vx) + A2 cos (vx), where m and n are…

A: We will find out the required values.

Q: The solution of the differential equation using variable separable +8 sec y = 0 is da dy O siny = 8x…

A: Divide by secy and multiply by dx the get the variable separate

Q: 1. Draw and obtain the differential equation of a circles having its center on the line x =y and…

A: 1.

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

A: Explanation  we have given the voltage change E across the heart satisfies the linear differential…

Q: Find the general solution of the first-order linear differential equation. e2x y' = 4 – e*y (Express…

A:

Q: State the order of the given ordinary differential equation. (sin 8)y" - (cos 0)y' = 9 Determine…

A: Find your answer below

Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

A:

Q: y > Ae* +Be* +ce; A,B and c unstant are

A: As per our guidelines we can solve only one question at a time please upload unsolved question…

Q: 1) Find the differential equation using method of undetermined coefficient y-3y' +2y e*sinx Aotoi…

A: Given: - The differential equation is, y''-3y'+2y=exsinx To find: - The solution of the given…

Q: 11. Obtain the differential equation of the family of parabolas y =x +c and sketch those members of…

A:

Q: Find the solution to the second order differential equation y'' = T COS(TX) with initial conditions…

A:

Q: 2. What should be A for the exact differential equation of ry + A , 2Ay – 1 dr+ y? Moreover evaluate…

A:

Q: Q-2. Form the first-order differential equation of ey = sinx

A:

Q: 1) y=x arccos - (c is an arbitrary constant), the lowest digit that satisfies Find the differential…

A:

Q: Q3. Second order non-homogeneous ordinary differential equation is given as: y"+ y' – 2y = x² - x+e*

A:

Q: Solve the 2nd order linear differential equation y" – y' = 5e* – sin2x %3D

A: The auxiallary equation for the given differential equation is given by

Q: The solution of the differential equation 2r -y = 3 represents a family of O circles straight lines…

A:

Q: What is the degree and order of the differential equation (y") + (y")° + (y')' + 8 = 0 O degree 3…

A: (y''')4+(y'')6+(y')7+8=0

Q: Construct a Differential Equation for the given equation y = a sin3x + b cos3x, by eliminating the…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² +…

A:

Q: Consider the nonhomogeneous second order differential equation a°y" – xy' + y = nT +0, x > 1.

A: First we have to find the general solution of the differential equation x2y''-xy'+y=xlnx where x≠0,…

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

A:

Q: In a spring mass system the displacement, x meters, of an object from its equilibrium position with…

A:

Q: The path travelled by a long period comet as it passes near the sun is described by a hyperbola.…

A: Given- x-3ydx-3x-3ydy=0 and the boundary condition is y=1 at x=-1. To Find- The unique curve which…

Q: The path travelled by a long period comet as it passes near the sun is described by a hyperbola.…

A:

Q: 9. Find the critical points of the autonomous differential equation dy dr sketch a phase portrait,…

A: Given: dydx=y2-y3 To find: Critical points

Q: For the differential equation y' = 2y - x, draw line segments representing the slope field at the…

A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

Q: Q-1. Form the second-order differential equation using the parametric definition of y = asino, x…

A: Given that: y=asinθ, and x=acosθ

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.