ди If u = e* siny where x = st? and y = s²t. Find ди and at as

Q: az Let z=xy-e'siny, x-uv, y=7Vu?+v?. Then at (u,v)=(7T,0) is du

A: Given that z=xy-exsiny, x=uv, y=7u2+v2find ∂z∂u at u,v=7π,0

Q: Exercises E Set 2] Implicit Differentia tion Find dy if dX 1. + Sin xy

A:

Q: dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression…

A:

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

A:

Q: dy 5. Find dr if y = sin(V +1).

A:

Q: Fiud ť amalytic Ť Ref = (t+y) · cos(2=y").

A: The objective here is to find f analytic. Ref=x+ycosx2−y2

Q: dy Find if cos(xy) = x2 + y?. Show your work. dx

A: Differentiate wrt x

Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

A:

Q: 118 t' sin (2€) dt

A:

Q: dy if y=| cos Ode dx if y= [ cos Od0. Use the Fundamental Theorem to find 3

A: We will use newton leibniz theorem to answer the given question .

Q: Find all x and y between O and 27 so that the equation is true. cosx+i siny = sinx+i x = 4 or 4y = 2…

A: Explanation of the answer is as follows

Q: +tlnt +tInt If x=sin and Jy= = cos prove that y"=c constant +eco te'

A: Given: x=sint2+tlntt4+etcost and y=cost2+tlntt4+etcost

Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

A:

Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

A:

Q: Eliminate the arbitrary constant/s of this equation to obtain the DE. Express the DE in general…

A:

Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

A:

Q: Write the DE, e" y' + e2y= sin a in the general form.

A:

Q: Laplace £& cos'at} Cos al t 81

A: The Laplace transform of the function f(t) is represented as F(s), it is defined as ∫0∞e-stf(t)dt.…

Q: a) u=r³-3ry² + 2xy + x, D) u= x² - y² +5, c) a= sinh rsing, d) u = e(y cos y + x siny), e)…

A:

Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),…

A: We have to find dsdtt0=π4

Q: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

A:

Q: s2 Q.3) Prove that L-1 () =(coshat sinat + sinhat cosat) 4+4a4, 2a

A:

Q: i? た(uパ) : tan ニ u= X Cosy V= X siny JR Determine Jf to 24 つメ

A:

Q: 22) pind tue indefnite ingegrel of fue followring fuchin cose dx Sin e 6

A: Using substitution method to find integration

Q: Differentiate. H(t) = cos2(t)

A: answer = -2sin2t   explanation is given in the below step

Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

A:

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y&lt;0 and we need to prove that | eiz | &gt;1 For b part, we need…

Q: cos e de =_ %3D • 2 • -T • 6

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

Q: a) Find dz, if z = e' sin e %3D b) Verify uxy = uyx , if u = In /x² + y² . %3D

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

Q: Show that z- sinh z Rcs :* sinh z

A:

Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

A:

Q: Inside the circle r =3 sin 0 and outside the cardioidr 1 + cos 0

A: The area that we have to calculate is the shaded area in the diagram above.

Q: Use a computer algebra system to evaluate (x2 – 2xy) dS. (Round your answer to two decimal places.)…

A: Here we solve the given calculus problem.

Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

A:

Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

A:

Q: (a) If f(x,y) = e" siny – e" sinx then verify that fry = fyz-

A: This question is related to partial derivatives.

Q: I sin(z) cos I) COS(2C (x) dx %3D

A:

Q: Fred show that Coshz-Coshx Cosy s +i Sinhx Siny O Coshiz= osz Sinh (iz)= j Sinz

A:

Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: E valuate:- seč (cosx) dXdy Sinly

A: We will have to evaluate: ∫01∫sin-1yπ/2sec2(cosx)dxdy.

Q: Find dy Sor The Sullowing Suetien? ) y = Cot 2) y = Ln [cosx) %3D

A: Please refer to the image below.

Q: Evaluate the Type II Improper lIntegral: M e cos 1-sin t da dx .

A:

Q: a sin a + In v ) da + tan adv = 0 Cos a

A:

Q: 1. f(t) = sinh? t

A: Given

Q: dy If y-3z sinh p z cosh y is exact, then n

A:

Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: Sexyz ds, C: x= 2 sin t, y = t, z= -2 cos t, 0sts T

A:

Q: dy If sinx + siny = xy, find dr coss-ly O a. -cosy cosx-y a-cosy none of these CORE-ty #coy CORE-Y…

A: The objective of the question is determine the derivative  and choose the correct option.

Q: Let y=4 In(cos(e3). Let y=4 In co: = Aeßt sinC (e3t) Then dt cosº (e3t) where A = B = C = D = I| ||…

A: y = 4 ln (cos(e3t))

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.