Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

Q: Use the characteristics method to determine the solution for the equation d2y/dt2 + dy/dt +3y = 0.

A: Dear student we are write the ordinary differential equation so  we use the characteristic equation…

Q: dy = 2t°y + y + 2t + 1. Show your work and explain thoroughly, when appropriate. dt Determine the…

A: To find the general solution of the given differential equation, first we separate the variables and…

Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

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Q: EVALUATE AND SOLVE THE LINEAR DE. d²x dx + 2,+ 5x = 8e¬ dt2 dt dx When t=0,x=0 dt 8 =

A: Given that: d2xdt2+2dxdt+5x=8e-t

Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: Express a general solution to 2x(1 – x)y" + (3 – 10x)y' – 6y = 0 Using Gaussian hypergeometric…

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Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

Q: Find the solution to the boundary value problem: Y dt2 dy dt +18y = 0, y(0) = 1, y(1) = 9

A: Given equation is the linear equation with constant coefficients.  So first assume the solution and…

Q: da Find at z = 4 if y = 4z² - 1 and dt da dt 11 > Next Question dy dt = -5. 11

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Q: * = x- 2y+ 2z = -2x+y– 2z dt dy dt E = 2x – 2y+ z dt

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Q: If  x2 +y2+z2  = 9,dx/dt  =5 , and dy/dt  =4, find dz/dtwhen (x,y,z) =(2, 2,1).

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Q: dx dt -x + y + 2et ip dt — у — е-t

A: System of differential equation

Q: Find the general solution of dy -my – ny³ dt by making a suitable substitution that transforms the…

A: Differential equation

Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

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Q: Find the solution to dy/dt = 6y Satisfying y(1)=7 y = ?

A: Firstly , separate the variables and then integrate and solve. ∫1ydy = ln(y) +C ∫tn dt =tn+1n+!+C

Q: If y=x² - 4x and x = √2r²+1; find dy dt when t = √2.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: y? what is dt/dy? 2y +1 if t =

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Q: Find the general solution of dt z(t) = Az where z = y(t and A =

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Q: Calculate dy/dt using the given information. xy2=4; dx/dt=-5, x=4, y=1

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

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Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the Euler method to solve d²y 0.5t + y = 0 dt2 where y (0) = 2 and y'(0) = 0. Solve from x = 0…

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Q: Find a general solution to the given Cauchy-Euler equation for t> 0. dz +13t +36z =0 dt2 dt

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Q: dr = -4rt whent=0, r=r, dt Obtain the particular solution of - %3D

A: we have to use separation of variable

Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: Assume Zero initial Conditions * d²y dy +3. + 2y = 0 dt2 dt

A: Solution:

Q: i need help to solve this: y''+ 5y' + 6y = δ(t-2) intial conditions: y(0)=0 ,  y'(0) = 1

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Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: 4d'y dt? dy -8y= 8e, find the solution dt a) Using the Method of Variation of Parameters

A: Given differential equation is 4d2ydt2−4dydt−8y=8e−t....1 We have find the general solution by using…

Q: dr = x – y +t dt dy =エ+3y +t+1 dt (20, yo) = (-4, 5)

A: Given that, dxdt=x-y+tdydt=x+3y+t+1 This can be written by, X'=1-113X+tt+1 Now the homogenous eigen…

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: Find a general solution to the given Cauchy-Euler equation for t> 0. dy +31- 63y 0 dt dr?

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Q: What is the general solution to the follwoing equation: (4t+5y+4)dt-dy=0

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Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

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Q: dz + et+z = 0 dt

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Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

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

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Q: Find the linearization of x = -1 f(x) = 3+ S sec(t – 1)dt at

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Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: Assume y′means dy/dt. Solve y′′+ 3y′−7y= 0

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Q: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

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Q: 4) Solve d²y + 4y = 2e¬t %3D dt2 Where y(0) = y(0) = 0 %D

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Q: x +y = x2 29) If - х - у + y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0?

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Q: Find the general solution of 0= -dy/dt -py-qy^5 by making a suitable substitution that transforms…

A: Given:- 0=-dy/dx-py-qy5 To find:- General solution of given differential equation

Q: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…