- (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with initial values :( )-

Q: Find the general solution of the given Ordinary Differential Eqauations system: - 9 x () where X(t)…

A: .Our general solution is of the form X(t) = C1V1eλ1t + C2V2eλ2t  where V1 and V2 are eigenvectors…

Q: What is the differential equation of the orthogonal trajectories of the family of curves x-3xy- 2y²…

A: This is a simple question based on differential equations which could be solved using the basic…

Q: Obtain the Differential Equation from the family of lines whose slope is thrice the y- intercept.

A:

Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: From the partial differential equation by elimanating the arbiraty function z=f(x2+y2+z2)

A: We have to form the partial differential equation.

Q: Suppose a student carrying a flu virus returns an isolated college campus of 1000 students.…

A: The number of students is 1000 and the number of students who have contracted the flu is x(t).…

Q: Find the differential equation of all circles with radius 1 and centers on the line y = x.

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Q: a. Circle of radius 1 and centers on the line y = x

A: The solution is given as

Q: 2. Form the differential equation from the circle passing through the origin having their centers on…

A: This question is based on forming differential equation by eliminating constant.

Q: In a differential equation where y is the dependent and x is the independent variable and the…

A: In a differential equation where y is the dependent and x is the independent variable and the…

Q: representing the family of circles through the fixed points (-c, 0) and (c, 0).

A:

Q: 5. Obtain the Differential Equation from the family of vertical parabolas whose vertex is at (h,k).

A: Formation of the differential equation

Q: Find the particular solution of the differential equation - ytanx e" secx that satisfies the initial…

A:

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A:

Q: Show that the solution of the differential equation (1–x*) = 2x(1+ y). dx 1+x given that y=1 when…

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Q: 1. (2x + y – 1)dy + (4x + 2y – 3)dx = 0; when x = 1, y = 2

A:

Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: A spring has a mass of 10 kg, is underdamped with coefficient β = 5 and its frequency is 0.8 Hz.…

A:

Q: Eliminate arbitrary constant from z=(x-a^2)+(y-b^2) to from the partial differential equation

A: Given z=x-a2*y-b2Hence number arbitary constant is 2 and number of independent variable is 2 . So…

Q: 21. Find particular solution of the differential oquation-2(x+ 1) Y.given x 0,

A: Givne that  The differential equation  To find the particular solution of the differential equation

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

A:

Q: What is the c value obtained for the special solution of the equation under the initial condition y…

A: Here we have to find constant of integration c.

Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

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Q: Consider the differential equation y' 2x - (A) At the point (- 1, 0.5), the direction field has a…

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Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

A:

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

Q: Write the general solution of (x² – x)y" + - 2x) y' -y = 0 about x = 0 of Hypergeometric…

A: Compare the given equation with the Hypergeometric equation of the form x1-xy''+c-a+b+1xy'-aby=0,…

Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

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Q: In each problem, obtain the differential equation of the family of plane curves described and sketch…

A: As per the guidelines we are suppose to answer only first question. Please repost the remaining…

Q: Suppose that a hare starts at the origin (0, 0) and runs with speed Vh along the y-axis toward a…

A: This question is from differential equation.

Q: What is the solution of the partial differential equation X

A: x∂z∂x+y∂z∂x=z is first order partial differential equation. For solution we use Lagrange's method…

Q: In a city of a fixed population of " people , the rate of change (with respect to time t) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to time…

Q: Obtain the differential equation of all straight lines with alebraic sum of the intercepts fixed as…

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Q: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

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Q: Form the partial differential equation by eliminating the arbitary function from z=xy+f(x2+y2)

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Q: Jesaki Inc will sell N units of product after spending $x thousand in advertislhg, as en by N = 74…

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Q: If the family of curve has 3 arbitrary constants then the corresponding differential equation is a)…

A: See solution below

Q: Suppose sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential equation…

A: To find the differential equation :-

Q: Match the differential equation with its direction field. y' = 5(x + y) – 1 -0.6- --0.4 - -0.2 0.2…

A: Given that y'=5x+y-1 Let fx, y=5x+y-1 then y'=f(x, y) As, we can see in given problem f(x, y)…

Q: 3] Form the partial differential equation by eliminating arbitrary function from z = e® f(x – y) -

A: Given: Z=exfx-y

Q: Verify that the indicated function y = (x) is an explicit solution of the given first-order…

A:

Q: Find the differential equation whose complete solution is y=c1e-x+c2ex+4x using elimination of…

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Q: obtained in factored form a linear differential equation with real constant coefficients that…

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Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: 27. Obtain the differential equation having the solution as the equation representing all circles of…

A: The differential equation of all circles of radius 1 and centers on  y=x

Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). ry" +6x²y" + 4xy' - 4y = 0

A:

Q: If the family of curve has 4 arbitrary constants then the corresponding differential equation is c)…

A:

Q: Find the differential equation of all family of circles with center at the line 3y - x = 0 with h…

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Q: Verify that the piece-wise defined function x 0' is a solution of the differential equation xy' – 2y…

A: