5. Find a solution f(x) to the equation (D3 – D² + D – 1)f(x) = 0 %3D such that f(0) = 1, f'(0) = 0, ƒ(7) = e".

Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: Suppose that f (1) = 1, f'(2) = 5, f'(1) = 4, g(1) = 2, g'(1) = 7. Find a. (fo g)'(1) b. (9((x)))…

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Q: Express (x + 4/x)dy/dx - y = 1 in the form y = f(x) where the curves passes through the origin.…

A: Given differential equation : x+4xdydx - y = 1                    ...........( 1 ) Multiplying both…

Q: Obtain the general solution to the equation (dy/dx)=(y/x)+5x+7

A: Given thatCompare to

Q: Vx6+7 (etan**) dy where ylny) = dx B) find (x2/3)( y v) sec

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Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: c If f" (x) = 18 cos 3x and f' (0) = f(5) = 1, find f(x).

A: The solution of the problem is given in the next step.

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: (y² + 1)(x + 1)dy = (y² + 3y)dx → Variable Sep.

A: The solution of a differential equation is defined as the function which satisfies the differential…

Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

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Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: Consider the curve given by y² = 2 + xy. dy dx (a) Show that = 2y-x (b) Find all points (x, y) on…

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Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: f(t) = 2t2 - 5 sin(3t) %3D L{f(t)}

A:

Q: 2- [10 points] Find the derivative dy/dx if y=3x +(5x ) (A) y=3°x +375 x² (B) y=3°*. 5 n 3+375x? (C)…

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ? 3x²y = x+y 3x²y = 2x-y…

A: Given the differential equation: x2dy+yx+ydx=0 with y1=1 To find out which function satisfies the…

Q: dfy = 12 - 30x, y'(0) = 7, and y(0) = 2. dx2 Find the function y(x) satisfying = 12 - 30x, y'(0) =…

A: Given:

Q: Find y as a function of a if y(0) = 19, y'(0) = 26, y" (0) = 14. y(x) = y"" - 10y" + 21y' = 48e²,

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Q: f'(x) = 6Vx ; f(1) = 7,

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Q: A dog is walking in a straight line on the road looking for bones. The dog is attracted to the smell…

A: The function x(t) indicates the position of dog with respect to time, t. So, the velocity of dog is…

Q: Solve dy (x + 1) + xy -x 0 dx

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Q: dx Find F(x) = S 1-2x+ 2x2

A: Here we solve the integration problem.

Q: (ii) y = e2x cos(1+2x²) (1+2x²)

A: y=e2xcos1+2x21+2x2

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

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Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: (b) Solve the IVP (3xy – y²)dx = (xy – x²)dy y(-2) = 3 - %3D %3D

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Q: Find g'(9) given that f(9) = 5 and f'(9) = 1. Enter the exact answers. (a) g (x) = Vaf(x) %3D g' (9)…

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Q: (dy/dx)-(x+3y)/(2x)=0

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Q: e-(2²+x³) dy dæ x=-0 Jy=0

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Q: dy = 4x -3 and y(4) = 0. dx Find the function y(x) satisfying

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