8. Find the solution y(t) of th d³y dy - 2y% = dt dt3

Q: (i) Construct the minimax polynomial p2 E P2 on the interval (-1,1] for the function g defined by…

A: As per the question we have to find the bset fit polynomial in p2 ∈ P , to to the curve g(x)=sin(x)…

Q: dx Solve dx dx +2 dt +x=3te¯' given x(0) = 4, = 0 at t = 0. dt %3D %3D

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Q: 2y" + 29y = 0, %3D y(0) = 7, y' (0) = 7. y(t) =

A:

Q: dy-(2y xe+2x²yex) dx (6 y3x -2x² e%) 1 the generl solution of the differential tion.

A:

Q: Solve dy (a) dx dy 1+y (b) dx 2x y+1 dy (c) (1+x 2+x dy (d) e*+y

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

Q: Find dy/dx for e 2x + y 2 = sec(2x) in terms of x and y using implicit differentiation

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Q: Show that the function f(1) = 5e²' satisfies y" – 3y' + 2y = 0, y(0) = 5, y'(0) = 10. %3D

A: The function ft=5e2t & the differential equation y''-3y'+2y=0 & the conditions y0=5,…

Q: S(y* - y-3)dy

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Q: -3x у" + 5y' + 4y %3D 10е'

A:

Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…

Q: Ex.: Solve dx dy 2=t.... dt dt dx dy -+2 +2-y=0... y = 0.. dt dt

A:

Q: (e* + 1)ydy = (y + 1)e*dx

A: Given differential equation is (ex+1)ydy=(y+1)exdx⇒ydyy+1=exex+1dx⇒1-1y+1dy=exex+1dx

Q: 7. Solve (a) y' = (5y²)-1

A:

Q: 5 +4y = 2 y(0)=1 dt

A: Given problem is:

Q: 4) dx + xdy = x²e" dy %3D

A:

Q: 3. Solve (x+y-1)dy = (x-y-3)dx 4. Solve dy/dx = (y+x)/x 5. Solve dy/dx +y = exp(3x)

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

Q: 9. Calculate y' for y +2xy = 3x-2y %3D

A:

Q: Find the general solution to 1 y' +

A: We have to find the general solution of y'+yx=1x4y34 .

Q: dx dt x(t) = = 3x(4-x), x(0) = 13 ㅁ

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.