If the substitution m = 3x - 2y was applied to the DE: =1+tan(3r – 2y), the resulting DE %3D dr would be:

Q: Solve the following by linear equation of order one: dy - (x3 - 2xy) dx = 0

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Q: dy 4x2-х-2 : У(1) %3D 1 dx (х+1)(у+1)

A: Explained below

Q: (D²-2D+5)y=e* cos x

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Q: 4x Compute (2x + 4yz) dz dæ dy 1

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Q: Solve the following ODE by finding an integrating factor for exact equations. (10 - 6y + 3e-3x)dx -…

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Q: Find the general solution of the following first-order ODE xy' = y + 2x3 sin?

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Q: Solve the given ODE using the method of variation of parameters d²y dy 2x + 2у — х4 cos x dx2 dx

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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…

Q: L(S,(3r² – cos t)' dt)

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Q: (5an 20 elan 20 sec²2 Bd ß 1. e?x +2e* dx e* +1 2.

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Q: dy - y = x y2 In x dx

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Q: The Bernoulli's Equation dy/dx - y[1/(2x)] - y^5 = O can be transformed in which of the following…

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Q: Find the general solution using substitution of the following DE: 1.) (2x + y + 6) dx + (2x + y) dy…

A: To Determine: Find the general solution using substitution of the following DE:

Q: Integrate the following using the substitution method. a) Te* cos e dx 2x+1 3x² +3x

A: We will use substitution method to evaluate these integrals.

Q: Se" cos 2t dt ,7L

A: integration.

Q: Determine the solution for this DE 2xy dx - (3xy +2y^2)dy = 0

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Q: Question 2 Evaluate: J y* sech (e m)tanh (e ), 7Iny @ -ch(v^) +C B) None -ech-(7) +C 7 ® ech (»*) +c

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Q: (t² +3) cos(5t) dt

A: According to integration by parts:∫udv = uv _ ∫vduWhere u can be choose in the orderInverse, Log,…

Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: Solve the following using the method of solving other substitution methods dy 2. dx sin(x – y)

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Q: ? cos i dt

A: You must have idea about integration by parts.

Q: z = cos(10xy) %3D dz %3D

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Q: Solve for the DE equation associated by the given function: а. у %3D Ае2х + Bе* + C.

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Q: Solve the DE by eliminating the arbitrary constant of x sin y + (x^2)y = C

A: Given that the expression xsiny+x2y=C. Differentiate with respect to x.…

Q: . Find the qeueral solution: - 2 dy +5y = ex Cos 2x

A: Complete solution = complementary function + particular integral.

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

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Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

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Q: y = In tan(x – A) +B

A: Some Important Formulas 1. ddxtanx = sec2x2. ddxsin-1x = 11-x23. sec2x = tan2x +1

Q: ds 1 s tan =cSC dt 2 2 2

A: We will find out the required general solution.

Q: dy = 6x– 2x + 1 cos y + eY %D dx

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Q: 1 and y' CO)

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Q: i?? cos(2t) dt csc(10t3)

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Q: 4 dy 5. х dx + бу %3D 3хуз 3xy

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Q: c) Se' sec (e - 1) dt

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Q: rl+cos(@) 3 6. Evaluate: 4r dz dr do 0.

A: We need to solve this cylindrical system

Q: Solve the following using the method of solving Bernoulli Equations. dy + y = e*y=2 dx

A: We need to solve the given differential equation by using Bernoulli's method.

Q: Solve for the particular solution of the ODE y" + 4y' + 3y = sin(e^x).

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Q: The general solution of the DE dx = cos?y is A y= sec?x В y=tanx + C y=tan-1(x) + c y= cos os-(x) +…

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Q: Find the solution of the D.E. below: xcos' ydx + tan ydy = 0 A y²+(tanx)²=c B x²+ (cosy)?=c © y?+…

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Q: Find the General Solution (D² – 3D + 2)y = cos(e¬*)

A: We need to find the general solution of (D2-3D+2)y=cos(e-x) Note the results  ∫cosx dx=sinx+C ∫sinx…

Q: Given: x = 4 cos 26 and y= 2 sin 26 What is the value of in terms of 6. dz O dy csc 29 dx2 -csc 20 O…

A: The solution is given below:

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: S' SE x² cos(xy)dxdy

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Q: Solve for the DE equation associated by the given function: у %3D Ае2* + Ве* + С. а.

A: the given solution of differential equation isy=Ae2x+Bex+C

Q: y" + 9y = e" cos 3x + x² + x³e*

A:

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

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Q: If Xy +y'=1, find at the point Co,-1) 4P dx 2 5- the value of

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Q: Solve the following using Integrating Factor by Formulas. 2. y(2x – y + 1)dx + x(3x – 4y + 3)dy = 0…

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Q: e/ (cos(2²) + y²) dæ + (sin(y²) + 2aæ²) dy Evaluate

A: In this question, we need to find the integral over C.  C is a closed curve with the boundary are…

Q: (10 – 6y + 3e-3x )dx – 2dy = 0

A: Topic - differential Equation