Integrate the following. Show your detailed solution. 1. S sin 30 d0 2. ſ csc 5t cot 5t dt

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Q: Solve the following DE: dy - 5y = 0 dx

A: The given differential equation is  a first order linear differential equation in variable separable…

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A: Given  -y dx+(x-xy)dy=0

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Q: Q1: Find dy/dx for the following functions (solve four only):- 4) y = cosh[sin-'(x²Inx)] (5) y =…

A: Here are the step by step solution of the given problems:

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Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

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Q: Solve the following bernoulli equation dy/dx +y/x =xy^2

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Q: 5. y = sin* x + cos* x

A: y= sin4x + cos4xdifferentiating w.r.t. x;dydx=ddx(sin4x) +ddx(cos4x)     =4 sin4-1x ddx(sinx)…

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Q: У(2ху+ 1)dx — хӑу %3D 0

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Q: (xy + 1)dx + x(x + 4y – 2)dy = 0 %3D

A: Given (xy+1)dx+x(x+4y-2)dy=0 Let the integrating factor be xαyβ Multiply both sides by xαyβ , we get…

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Q: Find by definition for the following : dx 1. y = (2x² + 1) 2. y = cosx 3. y = sin?x

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Q: Solve the following IVP: (3y cos x + 2xy^2)dx + (4y + 9 sin x + 4x^2y)dy = 0,  y(0) = 1.

A: The given Initial value problem is of the form M dx+N dy=0. After finding ∂M∂y, and ∂N∂x, we see…

Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

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Q: Answer the following. Complete Solution 1. Integrate -2 ex sinx a. dx 0 1+x² 62e

A: F = ∫02exsinx1+x2dxIt is a complex integration hence, numerical method is used.…

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A: Given that    dy/dx -(3/x)y = x4y1/3  Here we have to solve the given differential equation.

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Q: Solve the following Bernoulli equation. (* – 2xy dx + 3x²dy = 0 where y(2)=1.

A: Given, The Bernoulli equation y4-2xydx+3x2dy =0   Where y2=1 We have to solve the bernoulli's…

Q: B. Solve the following acrential equations using integration factor: 2. cos(y)dx= x(sin(y)-x)dy

A: Given problem:- B. Solve the following differential equations using integration factor:   2. cos…

Q: Find the solution of the following: 2. e2x (2cosy dx - sinydy) = 0; y(0) = 0 %3D

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the solution of the following: 2. e2x(2cosy dx- sinydy) = 0; y(0) = 0 %3D

A: The given differential equation is e2x2cosydx-sinydy=0 It can be re-written as…

Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

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Q: Solve the given DE: (yexy + cosx)dx + (xe*y)dy = 0.

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Q: Find dy/dx of the following: a. y=sinh-5x b. y=sinh-e* c. y = cosh¹ √√x

A: To find dydx for the given y.

Q: 4. Evaluate the following and give the exact value: m/2 (cosy sin(y + z) dz dx dy /6 Show your…

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Q: Find the general solution to the following equations: dy 2+ tan y dx

A: The given is the differential equation which can be solved as shown in step 2.

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A: Use separation of variables method on dydx=sinx2ex3 dy=sinx2ex3dx Now integrate both sides without…

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Q: II. Determine the solutions of the following DE. 1. (х — Зу + 2)dx + 3(x + 3у — 4)dy %3D0

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Classify and Solve the following x(dy/dx) + 4y = (x^4)(y^2) subject to y(1) = 1

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Q: Find the general solution of the following equations? X dy/dx + sinx - y =0

A: Non elementary integral: The integrals which do not have a solution can be represented using…

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Q: Solve the following using the method of solving Bernoulli Equations. dy 1. dx +? = x²y?

A: Given:         dydx+yx=x2y2 This is of the form dydx+P(x)y=Q(x)yn…