Solve the initial value problem. |y(x) = y + 4y = 0, 9 ---2, 2' 1 y (0) = y'(0) = 8' == y"(0) = 17, "(0) = 품 (51 cos(x) 131 sin(x)) e+ (43 cos(x)-63 sin(x)) et 64 25 8 ===

Q: Solve the following initial-value problem: y'+ (tan x)y=cos²x; y(0) = − 1 - O y=−(sinx)(sin x−1)-co…

A: We will find the required.

Q: Solve the following differential equation x²y" + xy' + y = cos(Inx)

A: Cauchy Euler's differential equation

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A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

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A: First order ordinary differential equation.

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: 11) Solve the following differential equation: (D² - 2D + 1)y= 2 cos(x)

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Q: Solve: (cos x) · (dy/dx) + y sin x = 2x cos2 x, y(Tt/4) = (-15/2-n2)/32.

A: The given differential equation can be written as :            dydx +ytanx = 2xcosx So, the…

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A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: Solvecos (2) O a. O b. 2 с. d. y cos Y I - [2 in (2) + co. (:)]* - = 0 dz y sin () = c C = сх ysin…

A: Given differential equation is yxcosyx-xysinyx+cosyxdydx=0       (1) Simplifying (1), we get…

Q: Sx2.- cos³ x-5 du 1-sin? x

A: Evaluation of the integral, bu using integral by parts

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Q: (b) If (20) = 3/5 and 0<o<T/4, find the values of i. sin (20) Cos ii, cos () iii. sin (0)

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Q: Develop a quadratic equation in x for the data point depicted as follows: (1,10), (4, 13), and…

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Q: y (3, 4) sin(0) = %3D cos(0) = tan(0) = csc(0): sec(0) : cot(0) = %3!

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Q: Solve the following ordinary differential equation y"+7e%y'+y=sinx

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Q: 4. y=sin(3x) • cos(2x), y'=?

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Q2/ If the following eq. is exact, then solve it (y cos x + 2xe") + (sin x+ x²e° + 2)y' = 0.

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: 3. Solve y' + cos(r)y = 2 cos z subject to the initial condition that y() = 2.

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Q: Find a general solution to the given equation. y""* - 4y" + 5y'- 2y = 8e* + + COS X Write a general…

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Q: (i) By sketching the graphs of y = 4 sin x and y= e" on the same coordinate system, find the number…

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Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

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Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

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Q: If y(v) = 10 COS 79 72 dr then

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Q: y"+y=82 (t) cos(t), y(0) = 0, y'(0) = 0

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Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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Q: Solve cos(2x) = v3 cos(x) – 1 where x E COS [-27, 27].

A: Given x∈[-2π, 2π]

Q: 1. Solve y' + 3x²y = cos(z)e with y(0) = -3.

A: Sol:- y' +3x2y=cosxe-x3A first order linear ODE has the form of y'x+pxy=qxy'x+px·y=qxpx=3x2,…

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Q: (Prove that A (B-A) = by stating all laws

A: