А. Find the general solution of the following first-order ODE ху' — у + 2х3 sin? (2)

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A: The Multivariate Newton Raphson method uses the formula: xn+1yn+1=xnyn-∂f1∂x∂f1∂y∂f2∂x∂f2∂y-1×fxnyn…

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Q: 3. [(3t +r*)sin (21)dt /

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Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

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Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

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Q: Find the general solution of y'=cos²xcosy

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Q: [-7, 1] The average value of cos (2z)e1-sin(2z) on is

A: The average value of the function f(z) on the interval a, b is  1b-a∫abf(z) dz.

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A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

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A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: Solve the ODE by the Euler method: given 2y" = -4y' - 1.5y y(0) = 3 and y'(0) = −2.5 with step h =…

A: To find- Solve the ODE by the Euler method: 2y'' = -4y' - 1.5y       giveny0 = 3 and y'0 = -2.5with…

Q: Q4/ Find only five of the following: 1-[t cos at 2-f(6 sin 2t – 5 cos 2t 6. 3+2S 3-[( 3 t5 – 2 t3+ 4…

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

A: Let's find integration of given function.

Q: e- + cos (xy) = (4 – 3z) (2 + 2.x), UIM 4. find ду ÚTM az cos (ху) — (4 — 32) (2- 8 UTM UT UTM

A: Partially Differentiate with respect to y

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A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

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Q: 1. Use the Euler, improved Euler and Runge-kulta methods to Solve the folllowing ODE s: 4 2 y =0 y…

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Q: Make the substitution v = ln x of Problem 51 to solutions (for x > 0) of the Euler equations in Prol…

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Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

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Q: 3) Find the general solutions only of the following higher order ODE by method of undetermined…

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Q: 5. Solve the given ODE using the method of undetermined coefficients. y" − 4y = x² + 4x − 3 -

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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: Find the solution for cos(x)" - (1 + x²) – 2xy = with the conditions dx2 1+x2 y(1) = -1, y(2) = 2…

A: Given equation is  cos(x)d2ydx2-(1+x2)dydx-2xy=11+x2 with y(1)=-1 and y(2) = 2 h = 0.25 To solve  -…

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

Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

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Q: (e²)(sin²2x) Compute In y and In 5z

A: Basic log formula are applied to solve the question.

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

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Q: 2. Obtain the general solution of the ODE (2a² – r²) dr = r³ sin 0 d0.

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

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Q: 21) (1 + cos 9t) 2 sin 9t dt

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Q: 1. Solve the hyperbolic function of the following. i. cosh (-2 + j3) in the form of a + jb ii. sinh…

A: some formula  coshx+jy=coshxcosy+jsinhxsinysinhx+jy=sinhxcosy+jcoshxsiny i.…

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Q: find a particular solution of y"-9y=-6 cos3x *

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Q: Find the general solution of the nonhomogeneous 2nd order ODE (Use the appropriate method) y" - 4y'…

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Q: 1%1… l.令 > OX 101:00 i learn.ejust.org/current, :D tan-(x) dx = %3D V3 n - In (8) - In (2) V3 None…

A: Since you have asked multiple question, As per our guidelines, we will only solve first question.…

Q: Show that y(x) = cos-(Acot x) + B is the general solution to the Euler-Lagrange equation for the…

A: Given function is, ∫1+y'sinx2dx Let, us assume that the function is, Ly',x,y=1+y'sinx2 So, the Euler…

Q: - Find the inverse Laplace of the following : 2s – 11 1) s2 – 4s + 8 3s + 7 2) s2 + 6s + 9 - - Solve…

A: As per our guidelines I am solving only first question with both parts please repost other…

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Q: 4e + 6x° + 9 cos z)dr %3D

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Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

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Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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Q: Enei Jan-19snk[(2n – 1)8] = %3D Select one: CO a. súnh(sink8) 4 Obsink(sink8) 4 3. o d. sinh(4sink8)

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Q: 8. Find the positive root of the equation 3x - cos x - 1 using Regula Falsi method and correct upto…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.