dy = 2t°y + y + 2t + 1. Show your work and explain thoroughly, when appropriate. dt Determine the general solution of

Q: find dy/dx

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Q: . (4fy – 152 – y) dt + (tª + 3y² – t) dy = 0

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Q: Q.1B) Solve the follwing diferential equation: 1 dy x dx siny + ycosy 2logx +1

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Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

Q: Show that the equation is homogeneous and find its solution. dy/dx=x+y/x

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Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1)=Q %3D

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Q: Solve IVP: dx x + Y, (0) = 0 dt dy 4x + Y, y (0) = 3. dt

A: Since you have posted multiple question we are supposed to give solution of first one only ...kindly…

Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

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Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

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Q: Provide the IMPLICIT solution as final answer unless EXPLICIT solutio (1) y' x(1 + y2); Provide the…

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Q: Find the general solution for y(t) where, dy 10t dt y II

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Q: b- Yt dt + dBt dY; 1-t

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Q: Q. 4. Find the solution of dx -10y 4e using variation of parameter method. dx %3D

A: We have to solve given problem:

Q: Show that the equation is homogeneous and find its solution. dy/dx = x+3y/x-y

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Q: Find dt y = 6t + /9+ 7-t dy dt |3|

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Q: dz Find given: dt Z = xe re4, a = t³, y = - 1+ 6t dz dt Your answer should only involve the variable…

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

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Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: utt = 0; x € (-0o; c0), t E [0, o) equation for u(x,0) = at

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Q: d'y dy dt Find the solution to the IVP + 9- + 18y = 0 where y(0) = - 7, (0) = 33. dt2 y(t) : Preview

A: Given that  The differential equation is  To find the solution of differential solution at given…

Q: Get general equation of this DE: (1 + y^2)dx + (x^2y + y + 2xy)dy = 0

A: Solving the DE by seperation of variables

Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

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Q: Find all solutions of the equation: dy​/dt=yt−y−t+1. Stationary and non stationary

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Q: rt%3Dr/6 t cos(2t) dt t=D0

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Q: dy Solve I +y= 1 given that y = 2 when t=0. dt

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Q: cos t dt t10 y = dy dz

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

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: Since wCo) = -2 in the diferential equation 3 dw + 6 w =g OBtain wCt) and explain dt Be haviort t =3…

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Q: The current in an electric circuit is given by the equation di Ri +L==0, dt - %3D where L and R are…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: dy х у ++1 y dx

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Q: -+y? сos(2t) %3D 0 ; y(0) = 1 dt

A: Given dydt+y2cos2t=0   y0=1

Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: dy +y=(x-1)y' dx

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Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

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

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Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

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Q: dy 2y = 2x/y %3D dx

A: The solution of the problem is given in the next steps.

Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: Solve the equation (x^2-3y^2)dx + 2xydy = 0 using y=v.x and u transforms

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Q: dx dy Explain your solution to the problem: = x + 3y – 2t², 3x +y+t.+ 5 dt ||

A: Given the system of differential equations:              dxdt=x+3y-2t2                  ......…

Q: d's 元 =-4 sin 2t-- 2 s'(0) = 100,s(0) = 0 %3D dt?

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

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Q: Q16 3⁰ 3t+2 a) 1 b) J dt dr cos² r√5 + tanz dt (3-5t)²

A: see below the answer and calculation

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: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: dy 26. + 2y = 1, y(0) dt ||

A: Given that differential equation we have to find the solution of given differential equation

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.