1. Solve: sin z cos² y dr + cos? r dy = 0, y(0) : (separation of variables) 2. Solve the linear differential equation: dr +r sec e = cos 8. de

Q: Solve the exact differential equation (in y -y sin x- без) dx + (— + сos x + 5 sec ytan y - бу)dy…

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Q: The differential equation y" – 3/ + y = 0 has y = cje(z/2) sin ( V3z ) + cze(z/2) cos as a two…

A: The solution is given as

Q: What is the integrating factor of the non-exact differential equation (4ху+ 3у?-х)dx + (x2+2ху)dy…

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Q: What is the simplest form of the integrating factor for the differential equation y' +…

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Q: Verify that for constants A, B, C and D the function ø(x) = Ae* + Be* + C sinx+ D cos x is a…

A: ANSWER :

Q: Solve the partial differential equation au sin xtan?y given that дхду ди = cos x when y= 0 and u =…

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Q: Solve the separable differential equation dy 8z – 6y Vz? + 1 dr = 0. Subject tn the initjal…

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Q: 2. Show that these differential equations are exact, then integrate to find the solution. (a) dy +y…

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Q: Use separation of variables to find the general implicit solution to the differential equation. 4…

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Q: 4. Find a third-order linear homogeneous differential equation which has the function r(t) = 3e-t +…

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Q: 1. ax дхду?, 2. dy + 2x+ y = x² + 2 3. дхду = y

A: Due to our guidelines, we can solve only three subparts plzz reupload rest question by mentioning it…

Q: 3. (D² +1) y=tan(x)

A: solve using Non-homogeneous Hihger Order Differential Equations: By the method of variation of…

Q: Find the explicit particular solution of the differential equation for the initial value provided.…

A: 1.Explicit relation : y = f(x) , No 'y' on the Right-hand side of the equation.  2. Particular…

Q: The equation, sin y-2 sin(2) sin(2y) y+ cos z + 2acos () cos(2y) = 0 is an exact differential…

A: We have to solve

Q: find the general equation and determine if separable variable, homogeneous, exact,non-exact…

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Q: the differential equation y''+ 9y = sin(3t) + 2 cos(3t), y(0) = 2, y'(0) = 1

A: Given y"+9y=Sin(3t)+2Cos (3t) --1y(0)=2 and y'(0)=1.Auxilliary equation associated to the…

Q: c) Find a homogeneous differential equation whose general solution is given by y = c,x-1 cos 3lnx +…

A: Let's find.

Q: Solve the IVP of differential equation and write the interval / a) where the solution exist, b)…

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Q: What could be an integrating factor in solving the differential equation dx (tan y) x = sin y ? dy…

A: Integrating factor of differential equation

Q: Use separation of variables to find the general implicit solution to the differential equation. 4…

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Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 17) cos(y) dy = 0 is given by In(x2 + 17) +…

A: To find- Show that an implicit solution of 2x sin2y dx - x2 + 17 cosy dy = 0 is given by lnx2 + 17 +…

Q: 4. Consider the differential equation dy arctan r sin(ry). dx (a) Find all equilibrium solutions.

A: From the given information. The differential equation is as follows.

Q: 4. determine the order of the given differential equation; also state whether the equation is linear…

A: d2ydt2+sint+y=sint

Q: 2xy' 2 tan(y) + (y')' (cosy)²

A: According to the given information, it is required to find the general and singular solution of…

Q: sec xdy – sin x sec xdx = 0

A: Using Differential equations.

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

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Q: Use separation of variables to find the general implicit solution to the differential equation. 9…

A: Given:       9 dydx=eysin2θysecθ

Q: ds 1 s tan 2 t =csC dt 2

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Q: y" +y = cos x ; when x = = 0, y = 0,y' = 1 %3D

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Q: )Show that given differential equation is exact hence solve it (cos a sin a - xy²) dx + y(1 – x²)dy…

A: We know that the differential equation  Mdx+Ndy=0 is exact if ∂M∂y=∂N∂x Given differential equation…

Q: azu Solve the partial differential equation du = 1 ax sin(x + y) given that at y = 0, and %3D дх ду…

A: The given partial differential equation is,∂2u∂x∂y=sinx+yGiven that, y=0, ∂u∂x=1 and x=0, u=y-12To…

Q: b. Find the most general solution to the associated homogeneous differential equation. Use cj and cz…

A: Here we will have to solve the equation which homogeneous. Therefore we will not take a Particular…

Q: dy/dx+(sinx/cosx)y=2cos^2sinx-1/cosx of first order linear differential equation y(pi/4) = 3√2 find…

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Q: Find the solution of the differential equation 1 y + sec 7 7 y = 8 cos 0 < 7 y(0) = 2 y(t) =

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Q: dy 1. da + Зу 3D 2ге 2xe-3r du

A: Using differential equations.

Q: Find the solution to the differential equation that satisfies the stated condition. sin (5x + T),…

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Q: 4. What are all solutions to the differential equation = sec? ? A y= tanr+C B y = sec x +C y = secz…

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Q: are constants. Find a homogeneous Euler-Cauchy differential equation whose general solution is C…

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Q: Solve the differential equation with the initial condition: (a) = 3t2 + cos t, y(0) = 12, (b) = sec?…

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Q: To solve the ordinary differential equation dy 3Y +5y2 = sinx, y(0) = 5 dx by Euler's method, you…

A: To solve the any ordinary differential equation by Euler method convert the equation in the form…

Q: Solve the differential equation cos(x + y) dx + (3y² + 2y + cos(x + y)) dy = 0. f (y). Express your…

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Q: A second-order non-homogeneous differential equation is given by d2y/dx2 − 10 dy/dx + 21? = 21x2 +…

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Q: The differential equation y" – y + y = 0 has y = cje(#/2) sin (3E) + cze(z/2) cos as a two parameter…

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Q: Find the value of k so that equation (9x^2 y^4 + sin ⁡y ) dx + (kx^3 y^3 - x cos⁡ y) dy = 0 is…

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Q: Find the solution of the differential equation that satisfies the given initial condition. y' tan(x)…

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Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = C₁cos (0)…

A: Sol:- While solving the question , initial θ is considered as 't' At the end , we will replace t…

Q: Use separation of variables to find the general implicit solution to the differential equation. 4…

A: Given that:  4dydθ = ey sin2θy sec(θ) So, by using variable separable, we getyey dy = 14. sin2θ…

Q: Two roots of a cubic auxiliary equation with real coefficients are m, = - and m2 = 3 + i. What is…

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