Find he value of ds/du at u = 2 if s t2 + 5t and t = (u? + 2u)

Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: y"(t) – 4y'(t) + 5y(t) = e"U (t – 2), %3D

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Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: FIND 2 DIFFERENT (LINEARLY IN DE PENDËNT ) SOLUTION S POR THE D.E y"_x² y'- 3 xy = O *y'-3xy%3D0

A: Step:-1 Given that y''-x2y'-3xy=0 ---(1) This is second order differential equation with variable…

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: ds if s = In [t*(t² – 1)]| dt 20. Find

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Q: s) find the general sduton of second dilferential equation 3y"+2y'+y=0

A: Consider the given differential equation 3y" + 2y' + y = 0

Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

A:

Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: 1. Solve the DE as follows: d'y dy +3 +2y = 24 y(0) = 10 and y'(0) = 0 di? dt

A: Given differential equation  is   y"+3y'+2y =24    ;    y(0) =10     , y'(0) =0

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: If y = t“, then dy 4t³. dt

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Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

A:

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: . Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) = Q Call

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Q: dy dt 1. y=V(3t2 - 2t + 1)(t2 – 1), 12/07/2021 18: 54

A: Given that       y = √(3t2-2t+1)(t2-1)  Here we have to find dy/dt .

Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: dz Find dt(t=1,s=0) when z = 2x3 + 15y3, where x = t2 - s and y =t+ 2s2

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Q: Solve for y(t) where y(t) + 2 / a – u)y[w)du = t.

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Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

A:

Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: dy dz 4 + Va Find for y =

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Q: Ex: Find and . fie 28. u = rs? In t; r = x², s = 4y + 1, t = xy³ %3D

A: ∂u∂x and ∂u∂y

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

A:

Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: dz (5) If z = u² + v² and u = at², v= 2at, find dt

A:

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: Q. Find F(s): e6t St2 cosh 4t dt.

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Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: If z = u2 v3 w4 , u = t2 , v = 5t − 8 and w = t3 + t, find dz/dt

A: Given,           z = u2v3w4 , u = t2 , v = 5t − 8 and w = t3 + t

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

Q: (D) If y/(t) + 2y(t) + Só v{r) dr = u(t - 1)

A:

Q: If dr/dt= -r5, what is r(t)?

A: Given drdt=-r5. The we have to find r(t) = ?