2V5 18. find In y 'dy dy 17. y + 4y In? y 2Vy de dt 19. 20. sec 0 + tan 0 tV3 + r + 2Vx – 1 dx 41³ – 1² + 16t dt 21. 22. 2xVx – 1 T/2 V1 – cos 0 do (sec t + cot t)² dt 23. 24. 6 dy dy 25. 26. Vy (1 + Vezy – - y) 2 dx dx 27. 28. xV1 – 4 In² x (x – 2)Vx² – 4x + 3

Q: DE 1. (-x)y-4xy +5y = cosx 2. d²u d'u 2x² at³ 3. d³x 12 des -2 d²x +(4t-1). + sin t dt² 4. √1+ (v)³…

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Q: 1 If f(x,y) = tan-(x y) with x= cos(2 t),y= then sin(2 t) " df can be calculate as follwos: dt O1.…

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Q: Given: a = 0 – sin 0; y= 1- cos 0 d'y Find: dz2 O d'y 1 dz2 (1-cos 0) d'y 1 %3D dz2 (1-cos 0) O dy 1…

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Q: 9. DETAILS SCALCET9M 3.9.010. If x2 + y2 dx = 9. dt dy = 8, find dt dz when (x, y, z) = (2, 2, 1).…

A: given,

Q: The solution of (1+y²) + (t- elan-ly Y =0 is: -1n dy %3D dt Select one: a. 1 t 3D elan-ly e2tan-ly O…

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Q: dy ) sin(t). (n + y) * cos(t), dt y("/3) = n, 0<t<"/2 4n V3n y = V3 * sin(t) – n cos(t) + n y =- 4…

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Q: dy dt (d) di² + 2- 3— 3t + 2, у(0) — У (0) — 0. dy (е) di? dy + 20y %3D —3 sin 2г, у(0) %3 у' (0) —…

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Q: 1 Let y = -. Find dy and Ay at x = 7 with dx = Ax = – 1. Enter the exact answers. dy = Ay =

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Q: Solve the IVP y" + y' + 1.25y = 0 with y(0) = 3, y/ (0) = 1 O e-t/2(3cos(t) + sin(t)) O e (3cos(t) +…

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Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: H.W.4 Find dy/dx for the following: 1) y= x+ sin x + sin 5x 2) y 32x + In (sin x) + In(sin 5x) 7) y…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 4. y" + y = tan x. 5. 4y" – 4y' – 8y = 8e-t 6. y" – 2y + y = : + 3e 1+ t2 et 7. 4y" +y = cos I

A: 4. Given, y"+y=tanx

Q: dy Nrite the linear DE (2y sinx – cos³x) dx + cos x dy=0 in standard form - +yP (x) =Q (x). dx (A)…

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Q: 22. If y = x+4 then what is 4Y? dx dy a. 4x(x + 4) dy С. dx -4Vx + 8 dx dy b. dx =-4(x + 4)= d. dx…

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Q: 1 Let y = -. Find dy and Ay at x = 8 with dx = Ax = –1. х Enter the exact answers. dy = Ay =

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Q: Which of the following functions is a solution of dx 12x – 8y dt dy 16x – 4y dt O a. æ(t) = et…

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Q: 15. ( dx +x'y = 0 15. xy 1+9x/ dy 16. (5y – 2x)y' – 2y = 0 17. (tan x - sin x sin y) dr+ cos x cos v…

A: We have to solve given problem:

Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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Q: d'y dt2 dy + 4 + 3y = 20 sin(t) where y(0): -2, (0): - 4. Find the solution to the IVP %3D

A: firstly we find out CF and then PI and  general solution is  y(t)=CF+PI

Q: A particular solution of the equation y(4) + 2y" + y = 9 cos(t) + 2e¬t – 5t is of the form Lütfen…

A: I have the rule for exponential function

Q: 1) y'- Sy of(4) t? ostL 2 ミf flel= ylo) =1 2) y"t Uy = ule - 2). sint y(0)=1 y'Co) =O >) F (t) + 2 S…

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Q: obtain the general solution. xcos^2 ydx +tanydy =0.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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Q: find dy/dt Y= (1+cos4t)^5

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Q: d*y 4)5t - dt4 +3r²( - (sin t)y = 0 -)³ – (sin t)y = 0 dt 5)(sin x)y² + 2 y = 3x' – 5 6) ху ? + 3 ху…

A: The order of the differential equation is the equal to the highest order derivative available in the…

Q: Find the solution of the following IVP. * (yexy) dx + (xexy + sin(y))dy = 0, exy + cosy - 1 = 0 O…

A: The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take y…

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

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Q: The solution of the initial value problem y" – 2y' + y = 10 sin(t), y (0) = 1, y (0) = 0 | %3D y =…

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Q: Н. W.4 Find dy/dx for the following : 1) y = x3 + sin x? + sin-1 5x 7) y = 3m (sec2x) eln(cos"*) 6…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (b) [(2t – n)0"dt ja- (a) x In x dx (c) 2x sin x dx

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Q: 1. S(tan -1)ʻ dp 2. sin2 B cos B dB .5 xdx 3. S (-7-8x-x* 4. Sx³ (a2 + x2) dx xdx 5. f (x²+a²)³ 6.…

A: (2)

Q: 3. Integrate! 12e dt a) ] 5e041 -0.21 b) c) f- dx 6r dr 3r? .$1+ In 3x² d) [Vcot*0 •csc² 0 do 2+…

A: Using Methods Of Integration

Q: Find the solution of the given initial value problem. y" + y = g(t), y(0) = 5, y' (0) = ? where 0si…

A: y"+y=gt, y0=5, y'0=7gt=t2, 0≤t&lt;63 ,       t≥6 Using the definition of Laplace transforms,…

Q: A 10 kg weight is attached to a spring with constant k = 160 kg/m and subjected to an external force…

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Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: 1. xy' + y = x* – 3x 2. x²y' – 2xy = x* + 3; y = 2 when x = 1 3. (sin20 - 2pсos0)d0 %3 2dp 4. ydx –…

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Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: 5) (D de with constant coefficients G 6) (D-6D+9)y= Ans.: y=Ce" +C,ue" +*. 7) (D' + D)y = tan x.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 3. - y = 5 with zero initial conditions (i.e. y(0) dy(0) = dt dºy(0) 'y(0) -0) %3D %3D Answer: y(t)…

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Q: Find dy/dt. 7) y= (ecos(u7)4 A) - esin(u7)3 B) co4 cos(/7) COS e3 cos(t/7) D) - sin e4 cos(t/7) Find…

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Q: 3 * (dx)/(dt) + (dy)/(dt) + 2x = 1, (dx)/(dt) + 4 * (dy)/(dt) + 3y = 0  Given x = 3 y = 0 when t =…

A: As per the question we are given the following system of differential equations : 3x'(t) + y'(t) +…

Q: Find the differential dy: y = sin(av). dy = " cos (av) [2v + a+i In a (1 + Ina p + x!+ In ¤ (1+ ln…

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Q: efe* cos 2t dt 1. 5. e 3 sin 2t 9. t S* sin at dt 2. 6. e' - cost 10. t e 3t | tsin 2t dt 1- cos 3t…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: 4 cos x Let y = [, (2t + 1) (t + 8t)'/3 dt. Find dy/dx.

A: We will find out the required derivative for given function.

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

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Q: 4. Show that al f(t) sin a(r – t)dt Y solves the initial value problem dy +a?y = f(x), dx? dy = 0…

A: The given initial value problem is                   d2ydx2+a2y=f(x), dydx=0 and y=0 when x=0. We…

Q: III. EVALUATE THE FF. ITERA •rU/2 ptan y sec y 1. . x' cos ydxdy Jo . cosy sin2x dy dx xp, •3n /2 pn…

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