Given f(x) = , 1+ cos²(t) t? - 9 dt %3D 0. At what value of x does the local max of f(x) occur?

Q: Example 64. Solve the simultaneous equations: dx -y3 e', dt dy +x = sin t, given x (0) = 1, y (0) =…

A: Given dxdt - y = et    --- (1)dydt+x = sin t   ---(2)with  x(0) = 1, y(0) = 0

Q: In Exercises 27-30, find the differential. 27. d(Vī-x) 28. d(e* + x) 29. d(arctan 4x) 30. d(8" + x)

A: 27. d1-x2 Ans.  ddx1-x2 =ddx(1-x2)12                         =  121-x212-1× ddx(1-x2)…

Q: Find general solution for y"+y=0.5cos(t) and state whether it is undamped, underdamped, critically…

A: The second order non-homogeneous  differential equation is y''+y=0.5cos(t) Solution for second order…

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: Find the function f(x) described by the given initial value problem. F'(x)=sin x , f(0)=-3

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

A:

Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: dy (2y-2) %3D dx

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Q: f'(x) = cos x; y (G) = 3 %3D

A:

Q: Solve the following differantial equation using finite difference method. d²x(1) + x(t) = 0 dt? dx…

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Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0,…

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Q: Find the function f(x) described by the given initial value problem. f"(x) = 3 sin x, f'æ) = 3, f(1)…

A: The objective is to find f(x), find the area of the region encloses by the parabola and the x-axis.

Q: If the function f (x) solves the initial value problem dy = (x +1)-1/2 – T · cos(T2) y(3) = 2 , %3D…

A: Given: dydx=x+1-12-π·cosπx Now separate the variables; dy=x+1-12-π·cosπxdx Now taking integral on…

Q: a) A capacitor (C) which is connected with a resistor (R) is being charged by supplying the constant…

A: Given : E = ∫0∞P(t) dt  ,   P(t) = 5Re-tRC2×R

Q: 9. Sinte)e x(t² + 1)dt = x ,(t² + 1)dt S' 2* dx < S, xdx 10. dx = dx + dx 11.

A: 9.∫ln(e)0ln(e)ex(t2+1)dt=x∫0e(t2+1)dt10.∫012xdx≤∫01x dx11.∫131xdx=∫151xdx+∫531xdx

Q: Solve the initial – value problem: xtan sec2. dy C :y(3) =0 2. eesc?ydx-Vr sinydy =0 :y (In's)= 3.

A: we can solve these question by variable separation and homogeneous function technique of solving…

Q: Determine weather the statement is true of false. Explain your answer.

A: Given: ∫cos x dx = sin x+ c∫cos x dx = (sin x + π) + C To find: Whether the  statement true or false…

Q: Find the particular solution of (cos x x sin x + y2) dx + 2xy dy = 0 that satisfies the initial…

A: Please see the explanation below

Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

A: The given differential equation is dxdt=t-sin(x), x(0)=1, h=0.1 The formula for improved Euler…

Q: Solve the initial-value problem: dy cos x - sin x + y, 0<x< 0.5, y(0) = 0 dx using a) Fourth-order…

A: Given function is                                                   dydx=cosx-sinx+y, 0≤x≤0.5 with…

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: The displacement of a structure is defined by the equation  y=9e-0.7tcos4t…

Q: If the function f (x) solves the initial value problem dy = (x + 1)-1/2 – r dx - T. cos(T2) y(3) = 2…

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Q: Solve the initial value problem given below. dy – 16xy and y = -2 when x = -4 %3D | dx

A: Given: dydx=-16xy, and y=-2 when x=-4 i.e. y-4=-2. To Solve: The given initial value problem.

Q: g(x, y) = sin (T ¤y) + log3 (x – 3y) -

A: The given function is                          gx,y=sinπxy+log3x-3y…

Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: 1-cos (t) B: Solve the D.E ý + 2ý + y = with zero initial conditions

A: Given y''+2y'+y=1-costt2with zero initial condition, i.e. y0=y'0=0

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

A: Note:-  For this problem if you want general solution for this problem then please resubmit problem…

Q: A 400 - V, 10 h.p (metric), 3 - phase synchronous armature resistance and a synchronous reactance of…

A: Solution...

Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: (1² +21) dx dt = = 2x + 2 (t, x > 0), x(1) = 1

A: Given that: t2+2tdxdt=2x+2 ; x(1)=1. Find the solution of this initial value problem.

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: Displacement Of A Structure Is Defined By The Following Equation For A Damped Oscillation: y = 9e^…

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

A:

Q: A uniform electric field of magnitude 400 N/C is directed parallel to and in the direction of the…

A: Given: Electric field of magnitude = 400 N/C Now, Electric field equals to the gradient:

Q: dy 1- Solve = cos x + y, where y = dx 2.0 at x 0 take step size h = Ax=

A: Given,         dydx=cosx+y Where y=2.0  at x=0   and h=0.1

Q: Solve the initial value problem. ds = Cos t - sin t, s dt = 4 %3D

A: According to the company policy, I'll solve the first question. Please resubmit the second question.…

Q: Find the function f(x) described by the given initial value problem. f'(x) = sin r, f(0) = 3 = sin…

A: NOTE: Refresh your page if you can't see any equations. . take integration  .................(1)

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: Use Euler's, Heun and fourth-order RK method to solve, dy :-2y +5e* dx = over the range x = 0 to 1…

A: Since you have asked multiple questions, we will solve the Question Q1 (a) and (b) for you. If…

Q: 1. Verify the initial value theorem for the voltage functions: a. 4+2 cos(t) b. t - cos (3t) and…

A: Given functions are a 4+2costb t-cos3t

Q: ds Find the particular solution of dt H|2 1 = cos-t

A: The given equation is;  ds/dt = cos (t/2).

Q: 1) Se2t cos(e') dt

A: Consider the integral  ∫e2tcosetdt

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

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Q: Find the general solution using the method of variation of parameters of the following: (2) y" – 3y'…

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Q: Solve the given initial-value problem. dy sin(x) + (cos(x))y = 0, dx -2 y(x) = %3D Give the largest…

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Q: Solve the given initial-value problem y' + (tanx)y = cos?x, y(0) = -1

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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…

Q: Q1: Find general solution of D.E. cosh (x) + sinh(x) y = e* dx

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Q: Find the general solution of (x + y) cos ydr + (a cos y - sin y)dy = 0. |3|

A: Differential Equation: A differential equation is an equation that contains one or more terms and…