Solve following ODE ( the integrating fac tor use メy+ 2y= uxL 2y-ux2

Q: (3 csc² t - 5 sec t tan t) dt

A:

Q: sec2 (sec-1 æ) dæ ævx? – 1 2 | Detailed solution, 3

A: Given: ∫32sec2(sec-1x)xx2-1dx

Q: y = Arctan ( 2+x 1-2x

A: We have to find derivative

Q: | (6x + 4) cos(3x +2) dx COS

A: Solving the given integral.

Q: Solve me initial No need to Jimphiry. by value the separaion of variables a.

A: To solve the following initial value problems by the separation of variables.a y'=1+y2, y0=1b…

Q: (D²+4)x=sin²2y|

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Q: 7) Solve y" +y = sec x

A: In order to solve the given question that is y'''+y=sec(x), we will first solve the homogeneous part…

Q: tan(z) + V3 = 0

A:

Q: Determine the form of a particular solution yp of Ур y" + 4y = x cosx. Do not solve the equation.

A: Here given the differential equation as y''+4y=xcosx or D2+4y=xcosx where D=ddx

Q: | x* (1–x)° dx

A: We have to solve the integration by beta function.…

Q: (x-7) dx 19. SJ5-4x-x2

A: Answer is following.

Q: dx 17. S√4e-2x-25

A: Given integral: ∫dx4e-2x-25.We need to evaluate the integral.

Q: Solve Variation of parameters to find y. and Yp and y y" + y = secxtanx

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Q: lve, using the method of variation of parameters: y/" + 4g/ sec 2.x

A: We will first find auxiliary equations and then find complementary solution to it.

Q: B. ty – (t+ 1)y + y = t²

A: Solve using variation of parameters :               ty''-t+1y'+y=t2            -------- (1)…

Q: 5. y= csc 5x 6. y = v2 - tan 6x 7. y = sec 2x - 3 sec 2x

A: Explanation of the answer is as follows

Q: х" In x dx

A: ∫xn ln x dx         We know that the formula for Integrate by parts is…

Q: y = x^Arctan *(x4)

A: We have to solve derivative

Q: y= sin (0.25) + sinh (2).

A: According to the question, we need to evaluate the function: y = sin-1(0.25) + sinh(2)

Q: Solve : 7tan³x – 21 tan x = 0 π 2π 4π 5π A B., T, c. D. 0,T, IT, 3'3 3' 3 7π 5π 6. 3 O A Ов O c OD

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Q: Q2/ solve :- +2y = Sin 3 X %3D u sing (D-operator methoD)

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Q: sin xdx 5t car? x

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Q: y = 2 sin 3x 1+3cos2x

A: We are given  y= 2sin3x/(1+3cos2x)  We have to compute y'.    Before computing y', let us first see…

Q: e"(cosh(2t)-cosh(5t))dt = ? -St

A: We will evaluate this integral using Laplace transform definition.

Q: y = Arctan (2x)

A:

Q: y" – 2y' + y = 1+a? 2

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Q: solve the equation by using Bernoulli's equations. y' + p(x)y = f(x) y ln y

A: Y’ +p(x)y =f(x)ylny divide equation with y both side we get y’ /y +p(x) = f(x) lny now consider lny…

Q: y = c sinx

A: It is known that ddxsinx=cosx and ddxcosx=sinx. We need to eliminate the arbitrary constant: c from…

Q: y= (sec ³x + tan ²x)

A:

Q: Q5) Solve the equation with y (0,1) = y (1,1) = 0 y (x,0) = sin x ! = 0,0 sxSI 8. ду (х .0) and…

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Q: y y'+y? x +1

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 3. f10x-sec(5x) tan(5x²)dx ans : sec(5x²) +c (VF). cot 4. dx ,note: Vx = xr ans : 2 In

A: ∫10x·sec(5x2)tan(5x2)dxlet u=sec(5x2)du=sec(5x2)tan(5x2)·10x  dxdx=dusec(5x2)tan(5x2)·10x Replace dx…

Q: •3 sech? x tanh x dx 2

A:

Q: I. Power Formula sec² xdx 1. S (1–4tanx)7 (2x+1)dx (x+2)*(x-1)* 2. S;

A: In this question we have to find the following integral using power formula. We know, Power formula,…

Q: 4. Solve for Y (s) given ty" + y' + ty = 0 y(0) = 0 %3D

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Q: Solve using variation of parameters: y" +y= cos r COS

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Q: Solve : 7tan³x – 21 tan x = 0 T 2n 4n 57 A.,I, C. 3' 3 3' 3 3 В.", п, D. 0,,,, 3' 3 3

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Q: J with 2 equations Give an exa

A: Let ax+by=0 and cx+dy=0. These lines pass through the origin. Then  ax+by=0cx+dy=0 is a homogenous…

Q: Solve using integration by parts de 3/2

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Q: sive a particular solution for y" - 2y' + y = z 1+x2

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Q: sec² i 6. dt

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Q: Pse Variation of Parameters to solve the DE y" – 4y

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Q: Solve for the arbitrary constant. Show complete solution. ln y = c1sin3x + c2cos3x + 9x2-2

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Q: sin(v3t) (b) L-- [tan- )) (a) L dt

A: In this question, we use the properties of Laplace and inverse Laplace transform, find the Laplace…

Q: i) Solve: (1+ yNdx = (tan-y- x)dy. %3D

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Q: y = tan e³x + etan3x

A: (tan x)' = sec2(x) (eax)' = a eax.

Q: eneral solution to the equation V2cosx = sin2x

A:

Q: Use variation of parameters to solve csc(t) y = et. sec(t).

A: Given: Let us consider the given y=12-121y+csctsectet and solve by using a variation of parameters.

Q: solve for general solution y''''=5 sin x

A: The given equation is y''''=5sin(x). The given equation is equivalent to D4y=5sin(x). Consider the…

Q: 1 dx, x3 – 1 (b)

A: a3-b3=(a-b)(a2+ab+b2) first we will do then partial fraction then calculate the integration.