Consider the following first-order ODE: (2xy – sec? x)dx + (x² + 2y)dy = 0 || Solve it using the method of exact equations

Q: C. Solve the nonhomogeneous ODE. y" + 2y' + 5y = x² + cos3x

A: To solve the following differential equation  y" +2y' + 5y = x2 + cos3x

Q: Q2/a) Find the integral f tan5x dx cos³x b) Find the integral cos*x dx 1-sinx

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Q: y-(x-5)2 + Sin-l XY 4.

A: To expand: y-(x-5)2+sin-1xyx+5.

Q: A. Solve the ODE: y"-2y' e"sinx

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Q: Consider the following first-order ODE: (y² + 2xy)dx – x²dy = 0 Solve it using the method of exact…

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Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: Solve the given ODE using the method of variation of parameters y" + 4y = sec 2x

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

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Q: 6. Identify the proper trigonometric substitution and then solve the integral 1 dx (x² + 1)²

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Q: +3Y=e

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Q: df (x) If f(x)= log,s 2 cos 4.x|+ sin x|, Then find 9 dx at x = - 6. -

A: Given, f(x)=logsec2ccos4x+sinxTo finddf(x)dx at x=-π6

Q: Find the general solution of the equation using method of undetermined coefficients. ODE: y" + 9y =…

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Q: Consider the following first-order ODE where y is the dependent variable and x is the independent…

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Q: (c) Show that e* sin(x²)dx < e – 1.

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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: Classify the following ODE and solve the initial value problem y(1-x2)y' = xy2 - cosx.sinx , y(0)=2

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Q: 4. Solve the ODE using Separation of Variables. X. dy - y = 2x²y dx

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Q: Solve the First ODE : (xy)(dy/dx)=x^2+2y^2

A: we havexy dydx = x2+y2    dydx = x2+y2xy                 --------- (1)we solve this equation by…

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

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Q: Find the solution of the equation cos y which tends to zero as r 00 and has the valRe cOS N Then r-0

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Q: (1+ In x) dx + (1+ ln y) dy = 0

A: Here we solve the differential equation

Q: Use the variation of parameters to find the general solution of the following ODE. z'' + z = tan2 x

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Q: sin x sin ydx+ cos x cos ydy = 0

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

A: Let's find.

Q: Express the function f in terms of the unit step function: sin(2t) 0st 2n.

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Q: Q3: Given f (x) = sin(x) cos (2x) and h = 0.5, find (numerically): Sf(x)dx а- b- f()(2)

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Q: fsinx cos/x Зл А 256 3 (В 512 (C) None Зл (D) 512 3 E) 256 -dx is equal to

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Q: - Verify whether the following ODE is exact and find its general solution. (2xy - sec²x) dx + (x² +…

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Q: Find the solution to the second order Linear ODE y" - 3y' + 2y = 10 sin %3D X y(0) = 1 and y'(0) =…

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Q: Solve the ODE using Galerkin method for two equal length elements d²U + 2 = 0, 0< x< 3 dx2 if u(0) =…

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Q: Derive the reductive formula for S sec" (x) dx.

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Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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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: Solve the following 1st order ODE. dy y sin x dx 2 cos x+4y²

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Q: Consider the following first-order ODE: x-y from x 0 tox 1.2 with y(0) -1 dx Solve using Euler's…

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Q: Q6. (A) Compute S[sec² (÷) – 1] sec*)dx. (В) Use Trigonometric substitution method to evaluate…

A: We will find the integrations as following.

Q: 1. Solve the following ODE using separable variable method: dy +(x+2)y³ =0. dx а)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

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Q: dy/dx+ytanx=cos^2(x)

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Q: Find e-t sin(v3t) (a) L dt (b) L-1 -1 tan

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Q: Q4. Solve the given ODE using the method of undetermined coefficients. - y" - 4y = (x² − 3)(sin2x)

A: Solution is below

Q: Q5. Use variation of parameters to solve the nonhomogeneous ODE. y" + 16y = sec'4x %3D

A: Given non- homogeneous differential equation is: We have to solve this differential equation using…

Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: 10. Solve the following ODES by separating variables (a) dx Cos 5t where x(0) = 1 dt x2 (Ъ) dy e2y+t…

A: Given: (a) dxdt=cos5tx2 where x0=1  (b) dydt=e2y+t To determine: The solution of given ODEs by…

Q: (10 – 6y + 3e-3x )dx – 2dy = 0

A: Topic - differential Equation

Q: What is general solution of the given ODE. * dy cos? (x – y+ 1) dx .2 COS

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Q: Is this correct?

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Q: Find F'(x). SOLUTION IN HANDWRITTEN|| 1 1. F(x) = √²2dt -2x-³ 2. F(x) = ²x²²x cos x² dx

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