1. f(x) = x², g(x) = 4|x]? %3D %3D 2. f(t) = 212 + 14t , g(t) = 2f² – 14t 3. f(0) = cos(30), g(0) = 2 cos³ (0) – 2 cos(0) %3D

Q: | (5e" + 4x° + 6 cos x)dx O 5e + x4 + 6 sin x + c O et – x4 + cos x + c - O 5e" + x4 – 6 sin æ + c O…

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Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: 1 the general solution of (y – cos² z) dr + cos z dy = 0

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Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: 3. Solve the following initial condition problems a. f'(x) = sin(2x)+ cos(3x), f(0) = 5 b. g"(x) =…

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Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

A: The given initial value problem is: dxdt-5x=cos4t with x0=5. The given differential equation is a…

Q: In y - e* + 2cos z = -3 In y +3cos z = 4- 2e* 2) e2x 1 +3 = +ln(z ex cos z +

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Q: 5. eу-2*(1 + x?)dx + сos y dy %3D 0, when x %3D 0, у %3D0 2e2* (сos y - sin y) + еУ(2x? + 2х + 3) %3…

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Q: The general solution of y" - 2y' +y= e* cos(x) is

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Q: 1. Show that y(x) = c; sin 2x + c₂ cos 2x is a solution to y + 4y = 0.

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Q: 3. Find the general solution of y" – 3y + 2y = cos (e~-).

A: We use the method of variation of parameters to find the solution of y''-3y'+2y=cose-x First we find…

Q: d²y Find the solution for cos(x) (1+ x²) – 2xy = with the conditions %3D dx2 1+x2 y(1) = -1, y(2) =…

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Q: 12 1 3. Find the exact value of the definite integral | dx (x+6) Vx- 3

A: The given definite integral can be evaluated using the method of substitution by making the…

Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: Suppose that x2y" + axy' + by = 0 has the general solution of the following form: y = x-(C, cos (3…

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Q: Solve the second derivative forf (x,y,z) = sin* (x² +y²) a²f ax? x²+y² sin ت )م(. (x² +y²' sin sin…

A: The given function is: f(x,y,z)=esinx2+y2z Differentiating it w.r.t. x: ∂f∂x=esinx2+y2z∂∂xsinx2+y2z…

Q: 6. Find the general solution of (cos cos y + ycos x ) dx + (sin sin x – x sin sin y ) dy = 0 x cos y…

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Q: Find the solution of the given initial value problem in explicit form. π sin(2x) dx + cos(9y) dy =…

A: Given: Now,                sin(2x)dx+cos(9y)dy=0Integrating both sides we…

Q: 1. Find the general solution (5x*y – sin (x))dx +(2x°y-cos (y))dy = 0

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Q: 2. xp- X2 a. b. + C с. + C d. None of the above dx 3. x(1+x) In xin (1+x")+C b. xarctan (1+x')+C a.…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

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Q: 3. 4. 5. π X dx sin() co₂ (:) ª 2x - 1 4x1 dx 8. 9. (x-1) √x dx _2_2x dx 10. S√₁-2² a x dx

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Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions on a…

A: Solution

Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

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Q: determine the annihilator of the givenfunction. F(x) = x cos 3x.

A: Consider the given function, F(x) =x*cos 3x. Let f(x) is a function, which is defined as,…

Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 2 cos 5x. a2. - 00 0, u(x,0)…

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Q: 6. Find the general solution of (cos cos y + ycos x) dx + (sin sin x – x sin sin y ) dy = 0 A. x cos…

A: Topic! Differential Equations.

Q: 3X 7- (0²1)y=K²" yp-e (4X-3} 8-(0-20+4)y=x+3x-5x+2 yp=Dx yo= 3.2 -2K 2. to-(D²+2}y=x²+xre+cos3X éte…

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Q: 6. Find the general solution of (cos cos y + ycos x ) dx + (sin sin x x cos y - y sin x = C - x cos…

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Q: 1- The integration of ſ cos . dx is: (a) sin를 + C (b) 2 sin +C coS x (c) 2 cos를+C (d) + C 2

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Q: Solve the initial value problem dxdt+3x=cos(2t)dxdt+3x=cos⁡(2t) with x(0)=−1x(0)=−1. x(t)=

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Q: 3 f(x) = x° – cos(x) %3D х — - Solve this question by the Fixed-point method on the topic of…

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Q: 2. Solve the initial value problem f"(x)= 2cosec3xcot3x +5 cos(-x)+3, given Зл = 4 4

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Q: (b) Find the solution for cos(x)- (1+x?) – 2xy = with the conditions 1+x2 y(1) = -1, y(2) = 2 and h…

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Q: 6) x²y" – 3xy' + 5y = 0 ;yı = x² cos(ln x)

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Q: Solve the initial value problem: f'(x)= cosx + sec2(x), f(pi/4)= 2 + ((√2)/2)

A: We have to solve the initial value problem where, f'x=cosx+sec2x and fπ4=2+22 Integrating both sides…

Q: 6. Find the general solution of (cos y + ycos x) dx + (sin x - x sin y) dy = 0 A. x cos y + y sin x…

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Q: The solution of the following exact initial value problem (y cos x – xy sin x)dx + (x cos x – 1)dy =…

A: does not satisfy

Q: Solve the initial value problem. dy + y sin x = 2x cos² x, dx y(0) = 0 COS X - 2.

A: Given: cos(x)dydx+y sin(x)=2x cos2(x)

Q: 1. [8te" dt 2. . (1–3x)sin(}x)dx 3. w'e*™ dw 1-1

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: [9] Find a 27-periodic solution u(x) of 5u"(x) + 3u(x) = f(x) where f(x) is a 27-periodic function…

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Q: Let y(x) be the solution to the initial value problem y" + 2y' – 3y = = -130 e-A" cos(5.x), y(0) =…

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Q: f(x) = |x|, −π<x< T 1-(-1)" a. f(x) = 2 Σ=1 sin nx n (-1)"+1 00 b. f(x) = 1 + ² =1 - 2 πT n² (-1)"-1…

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Q: Solve the initial value problem: dx/dt+2x=cos(5t) with x(0)=5 find x(t)

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Q: 37 a)/ 2x cos(x) dx he right end-points with 4 sub-intervals) 1 b) -2x2+ X-4) dx 5.

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Q: =1+ cos (x) x2 + 12x + 20 -dx 1 + cos² (x) 0. At what value of t does the local max of f(t) occur?

A: Given that f(t)=∫0tx2+12x+201+cos2 xdx To find the local maximum of f(t) at t:

Q: Solve the initial value problem dx/dt + 4x = cos(4t) with x(0)=-2

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Q: Solve the initial value problem dx/dt+2x=cos(3t) with x(0)=−1.

A: This is a first order linear Ordinary Differential Equation of the form x't+ptx=qt Integrating…