Consider the order and linearity of the following equations : I. (y +t) + y = 1 II. 3 + (t+ 4) y = t² + II. = cos (2ty)

Q: find dy/dx

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Q: Q1) Y"+5y"+9y'+5y=3e*2x solve the equation in method variation of parametric

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Q: Use the appropriate form of the chain rule to find the derivatives. w = 11x² + 11y² + z²; x = p sin…

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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: Q4: A particle is moving on the curve defined parametrically by the system of equation x = 1- 2cos?t…

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

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Q: Find the solution of the second order homogeneous linear equation when d2y/dx2-4 dy/dx - 4y = y ; y…

A: Given differential equation is d2y/dx2-4 dy/dx - 4y = y ; y (0)=1 ,y'(0)=2

Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: Determine whether the following equations are linear or non-linear? a. +y = 0 dt dx b. +x² = 0 dt dy…

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Q: find dy>dt.                                                        y = cos4 (sec2 3t)

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Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

Q: -2x b) y = Jrant V1 + t² dt tanx c) y = x² f, cos (t³)dt

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Q: Consider the order and linearity of the following equations: 1. (y+t)出+y= 1 II. 3 + (t+ 4) y = t² +4…

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Q: Determine the value(s) of r such that y (t) = e"t is a solution to y" + y' – 6y = 0.

A: Since part B and PART C are independent of PART A question.  As per the guidelines I am answering…

Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: Q5) Solve the system dx +y = et dt dy dt

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Q: y" – 2y' + y = –3 – x + x²,

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Q: Solve this equation: ди + a = at %3D u(0,t) = 0 %3D ди (L, t) = 0 az u(z,0) = 2 %3D

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Q: 23. (f + 1)dv/dt + 2tv =-1

A: Let's find.

Q: Solve the following separabledifferential equations: yy +x = 1, if y(1) = 1

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Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

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Q: Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y =sint cos…

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Q: Obtain the homogeneous linear equation satisfied by the following given function 1. y = 4e2x + 3e¬x…

A: The homogeneous linear equation satisfied by the given equation: Part(1):   y=4e2x+3e−x⇒3e−x=y−4e2x…

Q: Find the orthogonal trajectory of y=c ln x.

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Q: Consider the order and linearity of the following equations: I. (y+t)+y = 1 fy II. 34 + (t + 4) y =…

A: A differential equation is linear if the dependent variable and all its derivative occur linearly in…

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: Which of the following is/are linear equation/s of the first order? (2s e) ds = 2 (se - cos 2t) dt…

A: Topic- differential equations

Q: Find the conditions such that the equation M (x, y) dx + N (x,y) dy = 0 mogeneous and exact.

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Q: Consider the 2nd order equation 2²y+ Sin dy y² +y = Choose the ight assertion A) the linearized…

A: consider the 2nd order equation d2ydx2+sindydt+y2+y=0 this is a non linear homogenous differential…

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: Which of the following is not linear? a. 3. 2x + Vy? – Vz3 = 4 (sin T1/2)x1 + 4x2 = cos245 b.…

A: Which of the following is not linear? a 2x+y2-z33=4b sinπ2x1+4x2=cos245c 12x-y+πz=4d…

Q: Solve the following equation dy - 4t+ 6y = t3 +1 dt2 dt

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Q: Transform the equation 2r (y + 1) dr form of variable separable. - ydy = 0 into the %3D 2adr dy y-1…

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Q: -+y? сos(2t) %3D 0 ; y(0) = 1 dt

A: Given dydt+y2cos2t=0   y0=1

Q: Which of the following equations can be rearranged into separable equations? O y – y? = t - O y +…

A: y' + yt² = t² can be written as separable equation as : y' = t² - yt²  So, y' = t²(1-y) So, dy/(1-y)…

Q: Find the general solution of the given second-order differenttial equation y" + 18y' + 81y =0 y(x) =…

A: we have to find the general solution of the given differential equation. y"+18y'+81y=0

Q: Transform the equation 2 (y + 1) dr – ydy = 0 into the form of variable separable. O 2zdz y (y+1) dy…

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Q: Find the position function of a particle moving along a coordinate line that satisfies the given…

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Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: The two functions y1(t) = sin t cos t and y2 (t) = sin 2t are linearly independent. O True False

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Q: If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

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Q: The following equation describes the motion of a mass on a spring subject to damping, with a…

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

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

A: The solution are next step is

Q: dy Find -5 y%3D(2+cos4t) dy dt

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

A: We have to find

Q: The two functions y1(t) = sint cos t and y2 (t) = sin 2t are linearly Independent. True False

A: →Two functions y1 and y2 are said to be linearly independent,                 if, y1 ≠k y2 , where…

Q: A suitable substitution to transform the D.E. t dy – y dt = tydt into linear equation will be :

A: Substitution to convert given differential equation into linear

Q: dy + y dx dy – 3xy = 5y sin x xy dx2

A:

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.