h(x, y) = (2x sin(y)-e) i + ² cos(y) j r(u) = cos(u)i +2uj u = [0, π] E

Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(7x/2) = 0 %3D %3D f(x)

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

Q: y" - Y+1 = cos(+) u(

A:

Q: (a) fr = 4xz2, fy = yz and f; = xz 2 sin (x), fy = cos(x)y and f: = e" z z + y? If, f = = frâ + fyŷ…

A: a) Given f=fx+fy+fz and F→=fx x^+fy y^+fz z^ and  fx=4xz2, fy=yz, fz=xz So, we have f=fx+fy+fz…

Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: t y(t) = sin(WE) (t-c)² +wn² dł

A:

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

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Q: (c) y/" + 4y = 3r cos(2r)

A:

Q: y" + 4y – 5y = –260 sin(5x).

A: To solve the given differential equation

Q: y" + 9y = sec 3x %3D

A:

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

A:

Q: d dr -x² + e³¹ - tan(x) dy²-sin(y) dy cos(y) +2 d dx -√x+e²

A:

Q: cos y – sin y dy 1+ sin(2y)

A: Given: ∫cosy-siny1+sin(2y)dy

Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

A:

Q: (2 sin(y)) dx + (x y cos(y²)) d y = 0

A: Variable separable differential equation

Q: 3 x* cos(3 y) 2 x³ sin(3 y) dx + + 2 x2 ) dy = 0

A:

Q: If f (x, y) = x²y² + sin(xy) then fy (2,0) = 2.2

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Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: (b) | F. dĩ, where F(x, y) = (y cos(xy) – 2a, x cos(xy) + 1). 6 Y C 4 3 2 1 2 3

A:

Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

A:

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: cos(t)y'-tsin(t) = y ; is this seperable or non-seperable?

A: It can be shows that it is not separable. See the next step

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: (y2 cos cos x – sin x)dx + (2y sin x + 2)dy = 0 -

A: The given differential equation is first-order non-linear ordinary differential equation:   First we…