1. (a) Think about which method you want to use. Then solve the initial value problem with different conditions. Saf' = 4.x? – 2f (1) = 2 Sef' = 4x? – 2f (-1) = 2 and (1)

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: Solve: x'y" - 7xy' + 41y =0

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Q: x1 = X2 = Solve the following initial value problem: d 15 4 4et ²-(4 15 ) ² + ( 16 ) = dt 64 -16et…

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Q: (8x'y*) (-4x"'y) * (2x°y¯³)-

A: 8x3y-4-2-4x-1y-32x5y-3-2=-4x-1y32x5y-328x3y-42 [we first get rid of the negative signs from the…

Q: Find an 4.6. (3x²y + 2xy + y³) dx + (x² + y²) dy = 0 integrating factor and solve the following…

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Q: 40e5*, y(0) = ;, y'(0) =y"(0) 9. y" – 2y" + y' = 2 – 24e* + 2

A: Given: y'''-2y''+y' = 2-24ex+40e5x, y(0) = 12, y'(0)=52, y''(0)=-92

Q: 6) Suppose that the price of an Iphone (in dollars) is given by 6t p(t): 4 + 3e²/t . = 300 + t+2 t2…

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Q: x?S(x x] =0 2 2 x Can be wpitden as s" (o)= the Solu tion is

A: Note:- You have mistakenly written it as c1e^ax + c2e^-ax. At the place of a there will be α.

Q: Solve (x-1)' +(x-2)'+(x - 3)' +(x + 4)' +(x + 5)' = 0

A: The solution for the above question is as shown below.

Q: Solve 1 0-²40 = 5 x (0) = - 4, y(0) = 10

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Q: Solve for n  (1/p)=(pn-q)/(pn) + q

A: The equation can be written as follows.

Q: The time, in minutes, for a student to run L laps is T(L). What is the meaning of T'(3)=2? O When…

A: It is known that derivative of a function represents the rate of change of the function.

Q: If u(x) = x3, then du = 3x2.

A: