Q2) Find approximate solution up to 0(e*) for the equation 1) x - 2 + eex = 0 2) x + ev 2 +r = cos e

Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: 1. Find the general solution of y'= cos²xcosy

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Q: Find the general solution of y(4)+y'' = 3t2+4sin t-2 co

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Q: Is the ODE (sin(x-y)+1)dx=(sin(x-y)-2y)dy satisfied by the implicit solution x+y2=cos(x-y). Show…

A: An implicit function, however, is an equation that defines a relationship between two or more…

Q: 1- Solve = cos x + y, where y = dy dx 2.0 at x 0 take step size h = Ax= 0.1 and solve for 0 ≤ x ≤…

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Q: What is the particular solution of the function 3e" sin 5x – cos 5x? A cos 5æ + Bsin 5x + C'e" cos…

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Q: If x = sec e - cos e and y = sec" 8- cos"0 (x² + 4) (* - n°(y² + 4) = n²(v² + 4) Prove or disprove…

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Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

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Q: Consider the initial value problem sin(t)y" - ,y + r*y= In -, y(3) = -1, y'(3) = 57. Without solving…

A: Uniqueness and existence theorem: Let p, q, and g be continuous functions on an open interval I such…

Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: What is the particular eq. of the given: y"+9y=e^x (cos 3x)+ x² + x³ex

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Q: x³y"+xy'+4y = cos (2 In x)

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Q: Solve 2 cos (t) - con(t) – 3 = 0 for all solutions. where ke Z

A: solution of the eqauation

Q: Solve the diffevential cauationm. du e cosn=0,0 X2015,40)-a. Alam - Moislton method with h=0.4.

A: The given differential equation is, dydx+y-e-xcosx=0

Q: iii) E(-1)"+1 cos²(÷) COS n=1

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Q: (1+cos(4t) dt 2

A: Let's find integration of given function.

Q: Given that x(t) = c1 cos omega t + c2 sin omega t is the general solution of x'' + omega2 x=0 on the…

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Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

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Q: 7. Obtain the solution of (D² – 4)y = 16 + cos 2x using the method of undetermined coefficients %3D

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

Q: Solve the initial value problem: y'+2y = 40sin(t)+cos(t),      y(0)=6

A: Given,y'+2y = 40sin(t) +cos(t)y(O)=6

Q: what is the general solution of y''+4y=cos(2x)

A: Given: y''+4y=cos(2x)

Q: How can I find the particular solution of y''+36y=cos(6x)

A: How can I find the particular solution of y''+36y=cos(6x)

Q: 5. Find the general solution to the DE using the method of Undetermined Coetficients: y" + 9y = 2…

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Q: b) Show that the ode (x + tan-¹ y) dx + x+y dy = 0 is exact, then find the general solution and 1+y²…

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Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: The approximation of the solution x of the equation x In(x + 1)-x-2 0 accurate to within 10 using…

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Q: 1 ao et/2 dt = 0.50 2 An e-1/2 cos 2nt dt = 0.504 1+ 16n? 8n b, = et/2 sin 2nt dt = 0.504

A: a0 = (1/π) ∫0π e-t/2 dt , put -t/2 = x , dt = - 2dx Using formula ∫ et dt = et + c a0 = (1/π) ∫ ex…

Q: 3x)=てメ+cosス そし-て)- -4-cosいて) そしね)、ずした) ):-Smいて)=20348 Kntl = Kn - ぐし) 0.9651+2.0 348 32 Satisfied…

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Q: Compute e4 cos (r – 3) dr with two decimal places. Number

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Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: 9. Use the method of undetermined coefficients to solve the given system sin t X' X + %3D -2 cos

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Q: 4) One of the solution of the equation y"(x) + p(x)y' (x) + q(x)y(x) = 0 is given by yı (x) =…

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Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: 4. Solve the initial value problem (cosy)y' = sin²x cosx , y(0) = Give the solution implicitly. %3D…

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Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: 19. For all positive angles less than 360°, if csc(2x +30°) = cos(3y- 15°), the %3D sum of x and y…

A: Given that csc(2x+30°)=cos(3y-15°) It is known that csc(x)=1sinx. So, 1=sin(2x+30°)cos(3y-15°)…

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

Q: y'+ytan(x)=cos^2(x) ,      y(0)=-1

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Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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Q: 9 Solve: Solve Sut subject to + bux = 0 u(x,0) = +x² зик + 2х их = 0 subject to ✓****/ Rx [0,00) ản…

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Q: Apply Euler's method to approximate the solution of the initial value problem y' = 2 cos(2x) cos(y),…

A: We have to find the value of y(2) using Euler's method for approximation.

Q: Find the general solution Solution 8. y= c, +c, cos 2x+c, sin 2x- 7 e* cos 2x+ 85 6. e* sin 2x 85 8.…

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: 2. Solve the IVP y(3) + y" = 5 cos(2.x), y(0) = 3, y'(7) = 1, y"(0) = 0

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Q: Solve the initial value problem y′′ + 9y = cos(3x)+sin(3x) for y(0)= 2, y′(0)= 1.

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Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

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Q: Find the general solution of y''+ y =1/cos x

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Q: Find the general solution of cos(x) y' +sin (x) y = 2 cos^3(x)sin (x)-1 And determine the method of…

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