What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

Q: If y = Vx? – 2x then y' 2(x-1) 3x2-2x %3D

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Q: The values of C, and C₂ so that y(x) = C₁x + C₂ (-) satisfies the two conditions y(1) = 1 and y'(1)…

A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: 1. Let y = x2 + x +4+ Find y'.

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Q: Find y as a function of x if y(1) = 1, y'(1) = 4. y = x²y"-7xy' + 16y=x6,

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Q: 1+vx [8] Find y" of y =

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Q: Find y as a function of x if y" - 7y" +12y = 18e", y(0) = 25, y'(0) = 26, y'(0) = 25.

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Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: Calculate y" and y"". y(x)= y" (x) = y"" (x) = 10e*

A: The given function is

Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

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Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: Find a function y(æ) such that byy' = x and y(6) = 5. y =

A: y' = dy/dx y(6) = 5 means at x=6 => y=5

Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: Find y as a function of a if y"" - 12y" + 35y' = 24e", y(0) = 27, y'(0) = 11, y'(0) = 30. y(x) =

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Q: If t²y" – ty – y = 0 ,y(1) = 3 and y'(1) = -1, then y(4) = . . . %3D

A: Given differential equation, t2y''-12ty'-y=0,y1=3,y'1=-1 Find the value of y4.

Q: Find y as a function of a if y(0) = 19, y'(0) = 26, y" (0) = 14. y(x) = y"" - 10y" + 21y' = 48e²,

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Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

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Q: 2. 2xydx+(4y+3x²)dy = 0; y(1)=1 {y²+x²y³ =2}

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Q: If y = xsinx then prove that y''+y=2cosx

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Q: y′=2x/(1+2y),y(2)=0

A: To determine the solution of the initial value problem and determine its maximum value.

Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

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Q: Find y as a function of a if y(0) = 5, y(0) = 17, y"(0) = 5, y"(0) = 8. y(x) = y(4) — 6y" + 9y" =…

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Q: y (2 xy +1)= xy'

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Q: Find y as a function of x if y" + 16y' = 0, y(0) = 0, y'(0) = 4, y'(0) = -32. y(x) =

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Q: - 2xy³ + y² + (xy³ – 2y)y' = 0

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Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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Q: 1. Find y'. (a) v5æy + 2y = y² + xy³

A: Differentiate wrt x

Q: Find y' (x) if (3xy +7)² = 6y.

A: Differentiate both sides with respect to x and by using the formula for derivative of square of…

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.