Find ax and , if ay 9 11. f(x.y) = sin (y - x) 12. f(x.y) = %3D = tan por

Q: To obtain the General Solution of si What will be the form by separation of variables? cosv A)…

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Q: 3 Evaluate x² 2 SOFT S S x² sin y dy dz dx

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Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

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Q: Fial dy ldx by imphieit differention. X² (x+y)=y?(7x-y) 2. Find dy /x by implicit differention. e…

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Q: and Suppose z is a function of a and y, and tan Vy2 + x² = z*e6y. Solve for dx dy

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Q: 9. If y = sinh 4t and r = sinh t, show that 2 dy (a) (1+2²) = 16(y? +1), dr dy (b) (1+x²)- dx2 dy…

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Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: fas |(1+cos z)* dz

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Q: sinh x – 1 dx cosh x

A: The given integral: ∫sinh x-1cosh xdxWe need to find the antiderivatives.

Q: Find dy/dx by implic differatiation. b)e^xsiny=x+y

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

Q: 47. Let gd(y) = tan¬1(sinh y). Then 1 cosh y = d 1 sech y dy 8d(y): 1+ sinh² y cosh y where we have…

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Q: Evaluate Si S dz dæ dy 0. 4.

A: Here I am attaching image so that you understand each and every step.

Q: A. Find dy/dx of the following. 1. y = e" + eVinx + 2 In(ex) 2. y = er" 3. eln 4x + eln 4y = e + e"

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Q: 2.f(t) = cosh wt sin wt

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Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: Determine weather the statement is true of false. Explain your answer.

A: Given: ∫cos x dx = sin x+ c∫cos x dx = (sin x + π) + C To find: Whether the  statement true or false…

Q: • The integrating factor of the given DE are already given below. What is the value of "n" y²dx…

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Q: It is given that the metal has diffusivity a = 2.25, that the two ends of the bar are kept at…

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Q: cinxo ) 2X. dy dx Find for y= cos ( Inx + e

A: We have to find the derivative.

Q: borhem Solve Linear Disfenen tial Faul in dy 0+16 y= X simx X sin x ble it on ni

A: Compare with linear differential equation then solve

Q: olve the following initial value problem using variation of parameters: y" + 4y = cos 3x y(0) = 0,…

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Q: (ey + 1) cosx dx + esinx dy = 0 [Answer: (e + 1) sinx = = c] X (1 + e) dx + ež (1) dy = 0 [Answer :…

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

Q: (ylny - e¯xy)dx + ( + x lny) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact differential equation. If it satisfies the…

Q: Bernoulli’s Equation xdy − ydx − xy^3dx − xy^3 ln xdx = 0

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Q: 2y cos x + sint x)dx = sin x dy vhen x= t/4 ; y=1

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: Eliminate the arbitrar constant. 1. x cos(xy) + (e^x) ln y = c

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

Q: • The integrating factor of the given DE are already given below. What is the value of "n" y²dx…

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Q: * Q9 If y = cos(x + y)dx + (3y² + 2y + cos(x + y)) dy = 0, then M = cos(x + y), N = 3y² + 2y Ttue…

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Q: 10. f (x, y) = 1 sec(xy) in(rv)

A: Solution:-

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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Q: cos xdx (vii) S 5+sin2 x

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Q: 3. Evaluate 2y²sinxy dy dx 4. Evaluate , S sin(x² + y²) dy dx

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Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d.…

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Q: Find the general antiderivative of the given function. sin( x/7π)   and  sec2(5x) + sec2 (x/3)

A: GIVEN DATA : Function sinx7π and sec25x+sec2x3        TO FIND : Anti derivative of the function…

Q: 7. Determine the following general antiderivatives. cos (x) dx -dx sin(x) а. - b. 10 sin(x)cos(x) dx…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: 1) ydx + xdy = 0 3) (2x+e' )dx+xe' dy = 0 5) sinh(x)cos(y)dx = cosh(x)sin(y)dy %3D

A: We have to use properties of differentiation.

Q: 2.f (t) = cosh wt sin wt

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Q: 3y" – 6y' + 6y = e* sec x Target Solution: y = cief cos z + oze sin z+In(cos z)e" cos z +re sin z.

A: Given differential equation 3y''-6y'+6y=exsecx  We need to find the general solution of this given…

Q: r nosへSう'" ( メンン 2 COS(SIn (x))

A: Let, cos(sin-1x)=t⇒sin(sin-1x) 11-x2dx = dt⇒x11-x2dx = dt...(1)

Q: 1. Given xy = sin x , show that d'y 2 dy +=+y = 0. dxx dx

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Q: 56. Given that x+y - xy and that y dx dy when x 1 show that xy = e*

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Given Z = ye 3r + 2y; where a = ln 2 and y = 2 with possible errors Ax = 0.01 and Ay = 0.03.…

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