R - TVE + Vicsc(t) dt e tan (e) dr Vsec (e-) – 7 82y²-3g° (y² – y) dy

Q: y" + 2y + 5y = t cos(5t)-6,y(0) = 1, y'(0) = -2

A: Here we use the table of Laplace transform and the partial fraction method to find solution.

Q: cosysin2xdx – (cos?y – cos?x)dy 0 when y(30°) = 30° %3D %3D -

A: Solution is given below:

Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: Given z = 2t -41 and y=4 sin t %3D dy (i) da dy (ii) da?

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Q: e = (cos (y)+isin (y)) %3D O صواب İhi O

A: ez = ex+iy = ex (cos(y) + is in(y))

Q: -п/2 сп/2 w L cos dz dy de (ху

A:

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2

A: We can solve using Laplace transform

Q: y" – 5y' + 6y = 10e' cos t, y(0) = 2, y'(0) = 1 %3D

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Q: xy dA, where D = {(x,y) | sin x <y < 1/2,0<

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Q: y=6 In(cos(e7")). dy AeBt sinC (e7 dt Then %3D cosº (e7) where A = %3D %3D D = BCD

A:

Q: Given x 13t - 12 and y = 169 sin t %3D %3D dy %3D dx dy dæ?

A: Given that       x = 13t - 12   and   y = 169 sin t Here we have to calculate     dy/dx         and…

Q: T T 68. y = sin 3 + 4 %3D -

A: Given data:     The given expression of the function is: y=sin(-πx/3 – π/2)+4.     (a) The general…

Q: dy 2y ! = -x² y² sec²x %3D dx +

A: Using solution of Bernoulli Differential equation.

Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

A:

Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

Q: find dy&gt;dt.                                                        y = cos4 (sec2 3t)

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Q: d²i di 1 d. +R- +-i= E@cos ot dt? dt C a'v a'v ôy = 0 е. ôx

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Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

Q: dy Find xp x/3 y = cos () dt CoS

A: Given : y = ∫x3π3cost3dt

Q: f(t) = e2t – 2t² cos 4t + 3t sin 6t – 2t + 5 %3D -

A:

Q: Given z 13t 9 and y- 169 sin : dy dx d²y da?

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Q: (cos2y — Зx? у?)dx + (сos2y — 2xsin2y — 2x3y)dy %3D0 - |

A:

Q: ZX = 24, XY = 10, and YZ 26. Find cos Y. %3D 5/12

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Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

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Q: (c) y" + 2y-3y = 9 sin(t)

A: A detailed solution is given below

Q: cos t dt t10 y = dy dz

A: Known fact: ddx∫pxqx ft dt=fqx q'x-fpx p'x.

Q: SV1- x2 sin-1x dx

A:

Q: FIND Y(s) OF THE GIVEN EQUATION. y" + 4y = cos(t-3)+4t, y" - 6y + 15y = 2 sin(3t), y(3)=0_y' (3)=7 y…

A:

Q: cos(x + y), when x = 0,y = dx 2 = dy : %3D

A: To solve the differential equation we can use a substitution u=x+y and then we can use variable…

Q: dx dy. If y =x is expressed with parametric equations such that - 6when x=1, what is dt dt 12 -6 -12

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: d*y _2d'y dx d²y_gdy +4y = 0. dx dx dx Ans.: y= (C, +C,x)e* +C, cos 2.x + C, sin2x.

A: Given the homogeneous linear differential equation with constant coefficient is…

Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

A:

Q: -+y? сos(2t) %3D 0 ; y(0) = 1 dt

A: Given dydt+y2cos2t=0   y0=1

Q: (d) (.9.z) = arctan(y/F) + sin (3 + ry-5y).

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

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: (2^)u sec (VTt) 2V7t (a) y= tan dy: dt 5- v2 (b) y = 5 + v2 dy = -5- 2iv 5 -V-5-2iv5 %3D Need Help?…

A: Both the parts are given below.

Q: 3e2º sec 20 dy determine de Given y = V(0-2)

A:

Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: T/2 %3D cos (2wt + O, + ©z)dt = 0 -/2

A: The solution are next step is

Q: dt cos?(t) dr dx du du + ex- at cos²(t) :-7u, ex dr du -7u dr t(0) = 0, x(0) = a, u(0) = e et heR.

A:

Q: ,u = TX, X - 1 %3D %3D (Cosuz 4 dy

A: Differentiation using chain rule

Q: Use the equation e = 2xyz+1 to find %3D az/əx and əz/ay.

A: We have to find

Q: The ( 2e4t sec² e4t dt is {A} tan et + C {C};et tan e*t + C {B}- sec³e4t + C {D}e*sec® 4t sec3e4t +…

A: First substitute e^4t =u Then simply integrate

Q: y"+2y'+5y = 10 cos t, y0 = 2, y'0 = 1

A: Differential Equation: y''+2y'+5y=10 cos ty(0)=2,y'(0)=1The auxilliary equation…

Q: dy -2y 3cos3t – 11sin3t dt? dt

A:

Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

A: