Given that cos(x) = (-1x2 for e

Q: Зx + log dy find dx If y = 4 — Зх -

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Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: y = log (cos(2x) );y'=* %3D %3D O 2 tan ( 2x ) / In (10) O - 2 tan ( 2x ) / In (10) O 2 cot ( 2x ) /…

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Q: Solve: sin(y) dy/dx = e

A: given question is solved using variable separable method of differential equation    final answer is…

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: (a) In(1– x) +xe? (b) 2х 2x 1-cos(x) (d) V1+x-1 Check and briefly explain how to avoid the loss of…

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Q: 16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of…

A: Given: A cylinder with radius, r and height, h. The formula for the volume (V) of the cylinder is…

Q: arctan x Xe fel Xaresecx d

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: If the function f (x) solves the initial value problem dy E (х + 1)-И dx -1/2 IT • cos(TX)

A: Givendydx=x+1-1/2-πcos(πx)

Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

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Q: Find if y = In x5 + e¯cos2x – lIn e?. dx | dy_5, esin²x-cos²x 4 sinx cos x dy 5 %3D dx e cos²x-sin²x…

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Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: e (sinh x dx + cosh x dy) = 0

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Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: 23x+3+42x-1 6. S dx 2x+3 In(sin x) 7. S- tan x | Voty csc' y dy 8. dx 9. x log 10 x e" dr 1 + e" 10.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Solve the initial value problem (dx/dt)+2x=cos(4t) with x(0)=−2. x(t)=?

A: Solve the initial value problem

Q: Obtain the General Solution (x-1 )dx - (3 x -2y -S) dy = 0 MAM

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Q: / (3cosh m 2 cosh m sinh mdm +e°

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Q: 1) Find dy/dt for if : y = log2 (81'n 2)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Example 10.10. Using modified Euler's method, find an approximate value of y when x = 0.3, given…

A: We can solve this using given information

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: sin x – e-* = 0, [0,1]

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Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: 1 dy Solve the initial value problem of - 2 dx y +1 cos x , y(n) = 0

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Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

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Q: Solve the initial value problem dxdt+3x=cos(2t)dxdt+3x=cos⁡(2t) with x(0)=−1x(0)=−1. x(t)=

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Q: 2. In π 2 π ln - 4 e* cos(ex) dx

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Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: Question 18 Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+…

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Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: Use Euler's, Heun and fourth-order RK method to solve, dy :-2y +5e* dx = over the range x = 0 to 1…

A: Since you have asked multiple questions, we will solve the Question Q1 (a) and (b) for you. If…

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

Q: Question 8 Using Simpson's method 2 √ ²x³ dx for n = 4 is equal to

A: Simpsons rule

Q: 1. So dx 2. 3. x² (x+1)4 fxcos2xdx 4. TL TT TT Sễ sin²4ycos²2ydy sin*xcosxdx

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Q: y'+ytan(x)=cos^2(x) ,      y(0)=-1

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Q: =1+ cos (x) x2 + 12x + 20 -dx 1 + cos² (x) 0. At what value of t does the local max of f(t) occur?

A: Given that f(t)=∫0tx2+12x+201+cos2 xdx To find the local maximum of f(t) at t:

Q: 2/solve the differentialequation by using methad af Variation of (complete salution is vequired)…

A: Given equation is y'''+9y'=1cos11x               (i) Let us consider y'=z. Then, eq. (i) is reduced…

Q: Suppose we have a pendulum clock that uses a slightly damped pendulum to keep time (that is, b is…

A: At first we will derive a direct relationship between θ and m then from that we will observe how θ…

Q: y' cos x + y sin x = 2cos x sin x- 1 What is the particular solution when y(Tt/4)=3v2

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Q: Evaluate S 0 2-9.x² dx using the Gamma function.

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Q: ind the particular solution of (dy/dx) = (5x3 + x2 - 2); y = 1 when x = 0

A: The solution of a differential equation with no unknown constants is a particular solution of that…

Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

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Q: Solve the initial value problem dx/dt+2x=cos(3t) with x(0)=−1.

A: This is a first order linear Ordinary Differential Equation of the form x't+ptx=qt Integrating…

Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: - if eV = In(x) + In(y) + e³ ху 3 Find dx

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Q: Suppose that Newton's Method gives pn as an approximate solution of f (x) = 0, and we know that pn…

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.