Q.3 Use ODE methods to solve the BVP: U = 18xy + sin(2x- y) U(0, y) = y -cos y, U(x,0) = x² -cos2x, U,(0, y) = 3y-sin y

Q: Find the general solution. 1. (2xy-3x2)dx + (x2+2y)dy=0

A: According to company rule we can answer only first question and rest can be reposted

Q: 41. Let a, b, r be constants. Show that y = Ce-kt +a + bk k sin rt -r cos rt k2 +r2 is a general…

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Q: (X+2) fin ydx + 9x Cos ydy =0 check the comple tenett of the differential egation if not find Hhe…

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Q: Fial dy ldx by imphieit differention. X² (x+y)=y?(7x-y) 2. Find dy /x by implicit differention. e…

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Q: r) x²(esinx) s) e*[ln (cos x)] (m sin 3x t) e2x x COS X u) ex リこ Sm

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Q: Current Attempt in Progress dz Use an appropriate form of the chain rule to find dt 1 y = 7t z = 9…

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Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

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Q: 2n X f(p sin()cos(0) p sin ()sin(e) • p cos(o) p'sin (4) f(x, y, z) dV = dp de de Jn/2

A: SPHERICAL COORDINATES : The spherical coordinates are : x=ρsin θcosϕy=ρsin θ sinϕz=ρcosθJ=ρ2sinθ…

Q: f) y= xcos(xln x) g) y= 3(sin 2x – x* }** In. 3x'e** h) y= cosx

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Q: y = c1+ c2e“ + c3e¬“ cos(x)+ c4e¬ª sin(x).

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Q: 4. The current i(x, t) along a submarine cable of length L satisfies ixx RCi 0<x<L, 0<t = di -(0, t)…

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Q: Given (1+ 3x sin y) dx – x² cos y dy = 0 with y(1) = 0. Using Euler or Runge – Kutta method, what is…

A: Given 1+3xsin ydx-x2cos y dy=0....(1) with y1=0 We will find the value of fx, y to approximate y

Q: 02/ Solve the system derivative to find the general solution of each (x & y as a funtion of t). dr…

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Q: (d) Using the method of characteristics, or otherwise, find the general solution to yu, – x*u, = 0,…

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Q: Use the method of separation of variables to solve :=0 in (0,1) × (0,+0), (2) u(0,t) =u(1,t) =0,t…

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Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

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Q: (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 (y – cos?x)dx + cos x dy = 0 + Ri = E, where L, R, and E…

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Q: 2) Consider the DE: y" + 25y = 0 A) Verify that y = C₁ cos 5x + c₂ sin 5x is a solution of the given…

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Q: (+ > 0, => 0). -tz г () dt t=0 Know that (*) is true also for s > 0, and (- > , z = x e'y = x cos y…

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Q: Find the solution of Uxy - x²y = 0, Uy (0, y) = y², u(x, 1) = cos(x)

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Q: 1. 5. Find the value of the line integral. (x - y) dx- 2.xy dy C:r(t)=2 cos ti + sin ti

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Q: (1) xy dx- yx dy 0 (i) x cos ydx + ysin xdy 0 (i) cos xy-xy' sin xy] dx + 12xycos xy-xy' sin xy] dy…

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Q: Find the general solution of (1+cosy)dx-x sin ydy = 0. (1) x – sin y – x cos y = C (2) x = C(1+ cos…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: (In a + 12x y cos a + x*y cos x)dx + (8xy cos x + 2x"y sin x)dy = 0, 4 2 y(T) = 1/27 b. y da - a(a?…

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Q: 8.Using variation of parameters, solve for the particular solution of : (D² – 3D+ 2)y = cos (e¯*) O…

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Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: b) Find the potential P(x,y) attached to the exact ODE 2x sin(y) + x² cos(y) y' = 0 %3D

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Q: Q.1. Use the differential dy to approximate ay when y=3x-2 and x changes from 2 to 2.03

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: 12) dy dx - = x cos (6x²), y(0) = 7 A) y == sin (u) B) y = sin(6x2) + 12 C) y = sin (6x²) + D) y -…

A: In the question we have to solve the differential equation. Bartleby's guidelines: Please post…

Q: 2. Find a particular solution to each of these ODES by using the method of variation of parameters:…

A: Let's find.

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: Q1) suppose that W= x2+y2+z² and x cos 0, y = sin0, z = tan 0 ,use the chain rule to find de when 0

A: We have, W=x2+y2+z2 and x=cosθ, y=sinθ, z=tanθ  We have to find, dwdθ=? at θ=π4

Q: 1. y = Ax² + Bex 2. y = C₁ ex cos3x + C₂ ex sin3x 3. y C₁e* + C₂e²x + x 4. Iny = C₁e* + С₂е¯* 5. x =…

A: As you have asked multiple questions so that I have answered first question as per the guidelines.

Q: əz Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), y = u sin v, use chain rule to find : 2 ди Q4.…

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Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: 5) (D de with constant coefficients G 6) (D-6D+9)y= Ans.: y=Ce" +C,ue" +*. 7) (D' + D)y = tan x.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 1. x = sin(t)(3 – 2 sin(t)); y = cos(t)(3 – 2 sin(t)) sin(t?)) 2. x = cos(t²); y= e 1 1 1+t2 1+t² 3.…

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Q: find a particular solution of the given nonhomogeneous equation. a?y" + xy' + (x² – 0.25) y = 3.x/?…

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Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

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Q: (d) Using the method of characteristics, or otherwise, find the general solution to y-uy – xu, = 0,…

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Q: 1.) 201 4sin (x) cos (x) dx dy 0 y² + 1 [¹ylnª (y² + 1)

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Q: cos() y = 4 – t, z = CoS x = 3t, dz/dt using the chain rule. Assume the variables are restricted to…

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Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 1. z = 3x²y*; x = r^, y = r² 2. z =…

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Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.

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.