Find the value of k if 2 ydx+(3y+kx dy = 0 is exact. А. 2 В. 3 С. 4 D. 0 E. None of the above. O A O B O E 12. * The solution of the exact differential equation 3 x (3y +1dx+ 4x°y°dy =0 is A. x'y' +x' = C B. x'y' +x' +12r'y' = C c. 3x'y* +3x' +12x'y² = C D. 6.ry* + 6x +12x²y² =C E. None of the above. O A O B O D O E

Q: -(* +2) Solve for y = y (a) in the differential equation dy if y (0) = 1. No need to isolate y. %3D…

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Q: Show that the differential equation x³y² + x(1+yº)y'′ = 0 is not exact, but becomes exact when…

A: Given DE is  x6y7+x(1+y6)y'=0 ......(1) We first show that differential equation (1) is not exact.

Q: 14. Solve the differential equation dy dt y y(0)=1 by the Euler method with h=0.1 to get y(0.2).…

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Q: For the second-order differential equation y" + 9y = 6 cos x: a. Show that y = cos x is a solution.…

A: The given differential equation is: y''+9y=6 cos x

Q: Q1. Solve the differential equation of following 1. (y2 + 1) dy = 2 2. (D3 – D2 – 6D)y = 0 3. y" –…

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Q: 4- If the result we found in the analytical solution of a differential equation is 0.2556, and the…

A: The relative error is the error in the measured value. It is the ratio of absolute error to the…

Q: For the following differential equation = x * (x2 + y) + 2 and the following initial condition y(7)…

A: The given differential equation is y'=xx2+y+2 and y7=10. To find: the value of y1.

Q: For the following differential equation = x * (x2 + y) + 2 and the following initial condition y(7)…

A: We have to find the value of the approximate solution y1 by using Euler's method.

Q: A Bernoulli differential equation is one of the form dy + P(x)y = Q(x)y". dx Observe that, if n = 0…

A: Given - A Bernoulli Differential equation is one of the form dydx + Pxy = Qxyn . Observe that , if n…

Q: 1 3. y' -- %3D xy+x²y3

A: See the details solution in below

Q: а) x(0)--1,х' (0)-8 b) × () = },x (?) = o

A: x(t) = c1cost + c2sint . x '(t) = - c1sint + c2cost . x(0) = c1 = -1 . x '(0) = c2 = 8 . Thus, the…

Q: Eliminate the arbitrary constant of the given equation in order to transform it into a differential…

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Q: 6. Solve for the general solution of the differential equation using exact equation [2x + y cos…

A: We will find the Differential equation.

Q: For the nonhomogeneous differential equation y''-9y'+14y=3x^2-5sin(2x)+7xe^6x, determine the form of…

A: Given :

Q: Given the differential equation y ′′ + 2y ′ = x with the boundary values y (3.5) = 2 and y (4.5) =…

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Q: dy - 4sin( 2x) and y=2 when *=. What is the particular solution to the given differential equation?…

A: Topic = Differential equation

Q: The general solution of the differential equation y" – 9y = 0 can be written in the form y(x) =…

A: We have to find the general solution of the differential equation y''-9y=0 and write it in the form…

Q: 2. (a) Check that the first order differential equation 4x- dx dy - 4y =9(/xy² ) is homogeneous and…

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Q: Solve the initial value problem 2yy′+2=y2+2x with y(0)=8 1-To solve this, we should use the…

A: This is linear differential equation

Q: Which of the following is the solution of the Differential Equation with initial values?…

A: Here we will find out the required value.

Q: 2) y = c1e5x + cze²2×.-ex : y"-3y'-10y=6ex 2

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Q: Given the differential equation y' = e (2x –4) and the initial condition y(5) = a what is the value…

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Q: 13. Assume that the rate of change in is proportional to . Solve the resulting differential equation…

A: We use separable differential equation

Q: (20,00 Puanlar) 1- Solve the differential equation y' = Va +y– 1 (c+z) a)y = 4. (c-z) b)y = 4 (e+z)?…

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Q: 4. Solve for the general solution of the differential equation using homogenous equatiorn [x cos?…

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Q: We consider the following differential equations: xy" + xy' - (x − 3) y = 1 pour x > 0. Give the…

A: Consider the following differential equations: xy''+xy'-(x-3)y=1 for x>0   To Find: General form…

Q: Let y be a solution of the differential equation y' + !y = -2a°y^, where a > 0, y > 0 such that y(1)…

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Q: What is the value of y(0) if y(t) is a solution of the differential equation? 1 y' (t) + 2y(t) = 1…

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Q: Suppose y(3)=5 is the initial condition of a differential equation. Using Euler or Runge - Kutta…

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Q: %A) .{ The solution of the separable differential equation- None of the Choices y = 2² + 2 Option 1…

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Q: Show that the differential equation x³y² + x(1+yº)y'′ = 0 is not exact, but becomes exact when…

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Q: Solve the given differential equation: d²y dy tx- + sy = Inx dx dx?

A: According to the given information, it is required to solve the given differential equation.

Q: 2. Find a general solution for the following differential equation by undetermined coefficient. dy?…

A: To find the general solution of the differential equation by using undermined coefficients.

Q: What form of the particular solution is appropriate for the differential equationy "'- y'=4? A B C D…

A: To determine the form of the particular solution that is appropriate for the differential equation…

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Let y = emx is the solution to the differential equation, so…

Q: (25,00 Puanlar) dy 4- Which of the followings is the general solution of the differential equation,…

A: the given differential equation is dydt=t+y+1 the equation is of the form y'=p(t)y+q(t) y'=y+t+1 the…

Q: Select the general form of a particular solution for the differential equation y" + 4y =5 cos(2a). O…

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Q: 5) Consider the differential equation = , with initial condition y(2) = 3. Using Euler's method with…

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Q: 4. If y, (1) = a is a solution of dy dr Find the second linear independent solution and the general…

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Q: A student is solving a Cauchy-Euler differential equation and obtains the following solutions of the…

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Q: Given: (6x - 3y + 2)dx - (2x - y - 1)dy = 0. Find the general solution of this differential equation…

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Q: For the differential equation (D-2)ID+3]y = 10 e + 25e3*. What is the form of the particular…

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Q: [The following initial value problem is defined with an exact differential equation. If the solution…

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Q: 1. Let the following higher order differential equation y" – 2 y" – 3 y = 3 e5= (1). %3D Determine…

A: Solution by using the method of variation of parameters is given as follows :

Q: Show that the differential equation x²y³ + x(1 + y²)y' = 0 is not exact, but becomes exact when…

A:

Q: If y=3 when x=0 and y'=4 when x=0, determine the particular solution of this initial conditions,…

A: The given differential equation is                                                   y''-2y'-3y=0…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: The general solution of differential equation y''-3y'-4y=0 is given as y=c1e4x+c2e-x .Target is to…

Q: 14. Solve the differential equation dy t dt y y(0)=1 by the Euler method with h=0.1 to get y(0.2).…

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Q: Suppose x = cje= + cze³ a. Verify that x = cje + c2 e is a solution to x" – 2x' – 3x = 0 by…

A: A solution must satisfy its differential equation.

Q: –7 + 12 d5x 7) 25 d*x -7- dt5 d²x + 12 dt3 + 8. = 0 dt4 dt2

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