If y = f(x) is the solution of y'" – y" – 14y' + 24y = 0, f(0) = –4, f'(0) = 20, f"(0) = –44, then Select one: O a. f(1) = 4e² – 4e + e5 O b. f(1) = 4e2 – 4e³ + 1/e5 %3D O c. f(1) = 4e² -– 4e³ + e4 O d. All the previous answers are not correct. O e. f(1) = -4e² + 4e³ – 4/a4

Q: (D3 + D² + 4D + 4) y = 0 ; y (0) = 2 ; y' (0) = –4 ; y" (0) = 2. Find y (7)

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Q: 11. Find the general solution x(3xу — 4у3 + 6)dx + (х3 - 6х"у? - 1)dy %3D 0: а. (х + у — 2)3 %3 с (х…

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Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

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Q: Convert y " (f) + (1 – t) y' (t) + e¯' y (t) = t – 5t; y (0) =- 3; y' (0) = 4 into an in tegral…

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Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: 4. (D² +D-1)² y =0 ,when x= y = 0, y' = y" =1, y" = -1

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Q: If y(x) is a solution of (1-2-2xy +42y = 0, find the value of y'(1).

A: It is given that yx is a solution of 1-x2y''-2xy'+42y=0. The objective is to evaluate y'1.

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 6y = 3e t %3D Y(t) =|

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Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: Let a + 0 be any real number different from 0. If y = f(x) is the solution of y" – ay" = 60 – 60ax,…

A: Sine the statement true for any non zero a so we can choose a=1

Q: If y = x3 – 2x2 + 3 and x = t² + 2 find dy at t=2. dt %3D

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Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

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Q: • ex+y -2y-2=Ce e2x+y +2y-2%3DCEY e2xy -2y+23DCEY

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Q: Find the particular solution to D²y – 6Dy + 9y = e3x – ex when x = 0, y =y' = - 3 %3D

A: For given differential equation we have to find particular solution.

Q: dy Solve the initial value problem: + 2y = 6e¬x; y(0) = 8

A: Since the given differential equation is first order linear differential equation so we first find…

Q: for the implicit equation zey +In(y) = x³-12? da dy 3x2 02-2 = xey + Y 3x² - ey dy da xey + What is…

A: Topic = Derivative

Q: (D² + 4D + 4)y=0 when x = 0, y = 1 and y = -1

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Q: x' = -3x + 2y, y' = -3x + 4y; x (0) = 0, y(0) = 2 %3D %3D

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Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

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Q: Determine the general solution of (x-2y)dx + (2x+y)dy = 0

A: See the details solution in below

Q: Determine the value of k such that y=4x²-3e²t is a solution to x(1-x)y"+ (2x²-1) y'+k(2x-1)y=0

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Q: The function y(t) = 4e³t - 2e5t is a solution (but not the general solution) to y" + py' + qy = 0.…

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Q: The solution to the DE y' + 4y = e-4t; y(0) = 2 may be expressed as y = teat+ beat; find b-a.

A: The given differential equation is          y' + 4y = e-4t   . . . . . . . . . . (1)  The homogenous…

Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: The equation y² = cx is the general solution of: y' = 2x y': %3D у 2y A y' = 2 2y y' = 2x O D B.

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Q: Find the general solution of the following DE. y' = 3 (y + 1) O y = 3ce³x - 1 Oy = ce³x - 1 Oy =…

A: y' = 3(y+1) dy/dx = 3(y+1) dy/3(y+1) = dx dy/(y+1) = 3dx now apply both side integration

Q: 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

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Q: What is the particular solution of (2x -3y) dx + (2y – 3x) dy = 0 when x 0 and y = 1 %3D O 22 + y?…

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Q: Find the particular solution: y': 3(x² + √x) yez , y(4) = 0. ans

A:

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.