dy sin(x + y) dx

Q: Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

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Q: Let y = x. Find dy and Ay at a = 8 with dx = Ar = 1. dy Ay =

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Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: if x²+y²=t-- and x*+y*=t*+÷,prove dy dx x'y

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Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: Let v(x, y) cos(4x) sinh(4y). Find f(z)with Im( f(z)) = (x, y).

A: using the concept of cauchy - Riemann equations to find u and putting  the value of u and v (given)…

Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: (t + z cos(t)) dt + (sin(t) – 3z² + 5) dz = 0

A: Let's find.

Q: Find Fxx and Fxyz of: XX хуz y2+Cos (xz) f (x, y, z) : 2 Siny

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Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

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Q: If y=xtan(x) then dy at x = Tt is: dx

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Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: (a) Let I = dx. Show that I² = dx dy. R2

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

Q: dx + AIX y = cos x, y(n) = 0

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Q: Let Z = In X - y dz Find and dx dz dy

A: I have given the answer in the next step. Hope you understand that

Q: If y(u) = Cos v -dv then y'(u) =

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Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

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Q: sin x S ft) dt = Choose... 4. If f(t) dt = c, then / f(t) dt = Choose...

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sinh (xy - z2)

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Q: -s Jatx? 3. 4-/ sinx coss dx |

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Q: Let w = (sin(x) +7 cos(y)) dy ^ dz + (2³ – y cos(x)) dz A dæ + 14xyz da A dy. Find dw. dw = dx A dy…

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Q: dy IS let y = (cos r)m " then de sin z

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Q: 22. u- Vr? + s, r- y + x cos 1, s -x+ y sin t; ди ди ди when x= 1, y = 2, 1 = 0 ar ay at

A: Given: u=r2+s2  r=y+x cos t and  s=x+y sin t By using Chain Rule we have to find: ∂u∂x, ∂u∂y ,and…

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A sin x B sinx cosy =…

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Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Let v(x, y) = cos(4x) sinh(4y). Find f(z)with Im(f(z)) =v(x, y).

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Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: Let f(x, y) = 3e" sin(5y) af af dy

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Q: Find y', where t (a) y = Jo dt VE2 +1 (b) y /t² +t+1 dt 1 • sin²3x (c) y = | 1 dt t2 +1 Cos x

A: The given function is: y=∫cos xsin2(3x) 1t2+1 dt

Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y).

A: using CR equation we get....

Q: Let w = (sin(x) +7cos(y)) dy ^ dz + (z³ – y cos(x)) dz A dæ + 14xyz d A dy. Find dw. dw = dx A dy A…

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Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

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Q: Find dy/dx y = sec u, u = X- COS X -

A: Given : y = -secuu = x-cosx

Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: Find dy/dx y = -sec u, u = x- COS X |

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Q: y = x*, d'y 1 dy dx y dx, Prove that Y = 0. X

A: First we find out dy/dx then d2y/dx2. And put the values of dy/dx and d2y/dx2 in given condition.

Q: x²+y²` du du =+y dx If u=sin| ,x+y #0,Prove that x =tan u x+y dy

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Q: dx o ex+x е. f. S sin(vE) dt S dx 2x cos(vE) dt COS g. dx 'x

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Q: F(x, y, z) = (xy — 2², 2x+cos(yz), 2y² - sinz)

A: Given the vector field F⇀x,y,z=xy-z2,2x+cosyz,2y2-sinz . The objective is to find the divergence and…

Q: dy dt 1 Find dx if 2y°t + t°y = 4 and d.x Cos t

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