dy Nrite the linear DE (2y sinx – cos³x) dx + cos x dy=0 in standard form - +yP (x) =Q (x). dx (A) dy +y(2tan x) =cos²x dx (B +y(- 2tan x) =cos?x dx dy +y(2tan x) = – cos?x dx dy - +y(- 2tan x) = - cos?x dx

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

A: Given: 2ysinx -cos3xdx + cosx dy =0 Standard form: dydx+yPx=Qx

Q: dy Find if y = In x5 + e-cos2x – In e?. dx dy 4 sin x cos x dy 5 es sin²x-cos2 x dx e cos2 x-sin? x…

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Q: the general solution of the DE (cosxcosy+2x)dx-(sinxsiny+2y)dy=0 is

A: The differential equation M (x, y) dx + N (x, y) dy = 0 is exact if and only if  ∂M∂y=∂N∂x.   The…

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

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 2 cos x – sin xy; x = y = 8t t' Enter…

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Q: dx/dt + 4x = cos(2t), x(0) = -1 Find x(t)

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Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

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Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: Q1) Lind dy/dx of O xe 1o X +3y = 0 2 2sinx cosy=1 9 x = sec!

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; x y = 7t t' Enter…

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Q: Which one of the following differential forms is exact? a. x*ydx – 4xy²dy+2z²xdz O b. ety…

A: The differential in the form Mx, ydx+Nx, ydy is said to be exact if: ∂Mx,y∂y=∂Nx,y∂x In the…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; x = y = 7t t' Enter…

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

A: Given that      sinx siny dx + cosx cosy dy = 0 Here we have to solve the given differential…

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

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x : y = 4t t' Enter…

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

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; x = y = 6t t' Enter…

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Q: This differential equation is linear ODE in y. d'y dy y= sec(4y) dx A dx d*x - 5x = B dr ONone of…

A: Here in this problem we have to find which of differential equations in the given options is linear…

Q: a.) S (t² – 9) (4 – t²) dt from 2 to 3 b.) fx dx from 1 to 2 c.) f (x² - d.) f sin 0 de from 0 to…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

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: 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: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

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

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Q: A ) Find ſ cos 5t dt dy B) If y = x² +; , x= 2t -5 then find dt

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Q: z=cos y Using the substitutions the DE (3cos y – 5x)dx – 2x?tan y dy =0 reduces to dz = - sin y dy A…

A: Using given substitution.

Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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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: 3. у(3x3 — х + у)dx + x?(1 — х?)dy 3D 0 4. у(2х — у + 1)dx + x(3х — 4у + 3)dy 3D 0 5. (r + sin 0 –…

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Q: 1. + e*y² = x²y² dy da 2. y + sin x = x³y 3. In x - x²y = xy dy da + cos y tan a

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Q: Exercise: Solve the following differential equations: dy sin? y 1- dx cos2 x 2 - (1+x?)dy – 2xy dx =…

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Q: 1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – ee+xx-2dy = 0 3.x*ydy — ху?dx + 3ydy - 2xdx %3D 0

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Q: Find the general solution of the DE sec x dy = y dx. O In y = e^x +c O In y = sin x + c

A: Our Aim is to find the general solution of the differential equation given below:-sec (x) dy=y dx…

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: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: Given: X == In(x²y - 1) y Find dy/dx. dy dx x²y-1 y-1 (E) None of these 1 2xy dy y x²y-1 dx + dy dx…

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Q: 1 If y = sin' x then is dx dy dy -3 cos x b) dx a) –3 sin² x cos x dx sin¯ x dy dy _ -3cosx = -3…

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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: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x – sin xy; x = y = 2t t' Enter…

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Q: Solve the DE sinx siny dx + cosx cosy dy O by separation of variables. cs y = C sin x A В sinx cosy…

A: Solution

Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

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Q: Find the general solution to: dy d dx dy 1 dy Cos x + sin 2x dx x + 4 dx

A: d). Given differential equation is dydx=cosx+sin2x. Re-writing the given differential equation.…

Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 5 cos x – sin xy; y = 4t t' X = Enter…

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Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

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Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)

Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…