T: X-Y is differential operator 0 صواب İhi O

Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: du = t2 + 3u, t> 0, u(5) = dt 100

A: Given differential equation tdudt=t2+3u and u5=100 ⇒tdudt−3u=t2⇒dudt−3tu=t2t⇒dudt−3tu=t Hence, the…

Q: Ydx - xdy + x(2 - y)dy = y? ey dy %3D

A:

Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

A:

Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

A: Our objective is given below:

Q: How do you evaluate ∫ba r(t) dt?

A: Consider the given: ∫abr(t)dt Consider the first fundamental theorem of calculus: Let r(t) be…

Q: Is the given statement true or false? Justify your answer.   'The equation y'=x+y  is separable.'

A:

Q: (b) In(2x2 + у — 23) %3D х

A:

Q: z= f(x,y) ; x= r-s1 , y= r2s and zx(0,-1) = -24 ; If zx(0,-1)=-18, what is the value of the…

A: Given that z=f(x,y),     zx(0,-1)=-24 and  zy(0,-1)=-18x=r-s and y=r2s We have to find zr(0,-1).

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: F(x) = sin t dt, [0,1] 0. F(x)]

A: The following formula for Maclaurin's series expansion of sin x will be used: sin x=x-x33!+x55!-...…

Q: Q1. Let f(x, y) = x²y + x + y² +3. (a). Find f(x, y). (b). Find dy

A:

Q: Find the work done when a particle moves along the x-axis from x= 1 to x= 3 under the action of a…

A:

Q: T at = 8²T əx² with [B.C] T₂ (0,t)=0, T₂ (2,t) = 0 and [I.C.] 7(x,0)=f(x)

A:

Q: 47. Show that y = x³ + 3x + 1 satisfies y"" + xy" - 2y = 0.

A:

Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

A:

Q: Prob3: Find the derivative of the function at P, in the direction of A f(x,y,z) = (1.0.). = cos xy +…

A:

Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: For the function f(x,y) = 5x - 6y - 6, find - of and

A:

Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: дz Find and əx дz ду' yz + x ln y = z²

A: Given query is to find indicated partial derivatives.

Q: Which of these differentials is exact? (only one of them is exact) (1 – 2xy)dx + (x² + y²) dy O (22…

A:

Q: Solve the diferential eguation with discasfssic Of soaL (4xy-y2) dx +(2x? - 2 xy + 2y?) dy=o

A: Given the differential equation is 4xy-y2dx+2x2-2xy+2y2dy=0 This is form exact differential equation…

Q: Show that (∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

A: The equation to be proved is,

Q: The differential operator (D2 - 16D+113)³ annihilates the functions

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.