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

Q: Solve the following DE by using separation of variables or method used in solving exact DE

A:

Q: Given arccot(sin(2x + y)) + arctan(cos(2x + y)) = 0, solve for dx %3D dy

A:

Q: Evaluate by any applicable method. dx 0 x4+1 None of the choices. Please refer to my solution. O…

A: We have to find solution of given integral.

Q: 1. Given y= [In(3x² +8)] dy find tan(6x) dx

A:

Q: Solve the following equation using separation of variables: dy 2y- cos(x) dr 1+ sin(x)

A: Cross multiply the equation and solve

Q: Solve the following equation for the given conditions y(0) = -1,y'(1) = 2 d²y dy + 4 dx :+ 4y = sin…

A: Given differential equation is d2ydx2+4dydx+4y=sin2x+cos2x      (1) with y(0)=-1, y'(1)=2 Auxiliary…

Q: Find the solution of the equation =e* cos y d ig %3D dy? which tends to zero as x 0o and has the…

A:

Q: 3) I= dx 4) I= f cos?x dx

A:

Q: A particle travels along the x-axis such that its velocity is given by v(t) = (t25 + 4t) cos (3t).…

A: The velocity of the particle is given by: v(t)=(t2.5+4t)cos(3t)

Q: Find the solution of the equation cos y dy? which tends to zero as i → 0o and has the value cos y…

A:

Q: Answer the following neatly and completely. Find dy/dx. 1.y = sin(x²e3*) 2.y = In (tan x?) .xcos y –…

A: Chain Rule of Differentiation : If we have y=f(u) and u=g(x) then dydx = dydu·dudx

Q: e) tan 5y – y sin r+3ry? = 9.

A:

Q: Solve the following Initial Value Problem. (sinx)dy/dx+ycosx=xsinx   ,    y(pi/2)=2

A: It can be solve using the method of integrating factor

Q: Find the general solution to the following equation y" (0) + 3y'(8) + 2y(0) = sin 0 – cos 0

A:

Q: Solve the following D.E dy sin x +2y= tan³| dx 2 1 Add file

A:

Q: y'+y = cos(e*

A: Given equation is: y'+y=cosex

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

A:

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:

Q: Find the general solution of the following equations. 4. dy - x² = x dx sin x 5. y-'dy + ye cos x dx…

A:

Q: 3. Solve for fe)(r) given that f(r)% = sinh(3r)

A:

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

A:

Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

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

A: The objective of the question is integrate given data .

Q: 12. Solve the following first-order equations: dy а. = 4x/y, with y(0) = 1 %3D dx

A:

Q: b) Solve the following differential equatión . = 1 + Sin x + 4x dy +2y dx dx

A: According to the given information it is required to solve the differential equation:

Q: Solve for the general solution of the following equations: 2ydx + (x–sin Jỹ )dy =0 е.

A: Given differential equation is  2ydx+(x-sin√y)dy=0

Q: Show that the following equation is exact and solve it: (2y sin x cos x - y + 2y² exy²) dx - (x -…

A:

Q: Show that the following equation is exact and find its general solution. (3x²y+ 4y + dx + (x + 4x +…

A:

Q: 4. Find a general solution to the equation y' – 3y = e" sin(2x). -

A:

Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: LE (4y°x² + Sin 2x + Cos²3y) dy dx

A: we have I = ∫-11∫-2-1(4y3x2 + Sin 2x + Cos23y)dy dxlets slove each term separatelyI1 =∫-11∫-2-14y3x2…

Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

Q: d'y Using method of variation of parameters solve + 4y = 4 tan 2x dx?

A: d2ydx2+4y=4tan2x

Q: Q) Find the general solution. dy sin-1x Iny dx II

A:

Q: 2) I = fe-zx sin 2x dx

A:

Q: Check for exactness and obtain the general solution. 1. (2xy – tany)dx + (x2 – xsec?y)dy = 0

A:

Q: 4. Find du for the equation 3y? – cosy = x° -

A:

Q: implicitly, if e*(e» – 1) + sin(2x + 5y) = In(v7) – · cot(2x) 8. Find %3D y+2

A: Given,

Q: Solve the given problem below: (2x + y cos x) dx +sinx dy=0

A: We will solve it by exact differential equations method.

Q: Solve the following Bernoulli's equation by using an appropriate substitution. sin y (x + sin y)dx +…

A: We have to solve the give Bernoulli's equation by substitution.

Q: Find the smallest positive value of t. sin(2#t) = 4

A: Given sin2πt=32 To find the smallest positive value of t let 2πt=sin-132

Q: Find dy/dx for the following 1) y = x3 + sin x? + sin-1 5x

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Use any appropriate method to find the general solution of each of the following equations. dy sin 2…

A:

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

A:

Q: 1%1… l.令 > OX 101:00 i learn.ejust.org/current, :D tan-(x) dx = %3D V3 n - In (8) - In (2) V3 None…

A: Since you have asked multiple question, As per our guidelines, we will only solve first question.…

Q: evaluate the triple iterated integral.

A:

Q: 2. Given xy? =Sinlyz find dź/dk

A: We are given: x2+y2+z2=sinyz Differentiating both sides with respect to x, we have…

Q: Find the general solution (implicit explicit) to the following equation. or et y" – 2y' + 2y =…

A: We have to find the general solution of the differential equation y''-2y'+2y=exsinx.

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.