: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

Q: Solve dy dx =-y with y(0) = 1. Find y(0-01), y(0-02) by Runge-Kutta method.

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Q: Let y = tan(4x + 4). Find the differential dy when x = 4 and dæ 0.2 Find the differential dy when x…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 7x2 – 3 dy =

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Q: 18. y = x/I - x?

A: Differentiation:- The derivative of a function of real variable measures the sensitivity to change…

Q: dz b- Solve by chain rule to determine dx z = x²y* -2y , y = sin(x²)

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Q: Let y = tan(5x + 4). Find the differential dy when x = 5 and dæ = 0.4 Find the differential dy when…

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Q: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: Determine the differential of the function y=x3−3x2+4x at the point x0=1 when dx=0,1.

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Q: Find the differential dy. y = 5x2 / x-9       dy =

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Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A: To find: The value of dydx in terms of x and y. Given information: y=csct,x=sec-1t

Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y? + z²; x = psin o cos…

A: We have to find derivative of given function by using chain rule.

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 3x2 - 5 dy =

A: Given, y = 3x2-5  We have to find the differential dy for the given function

Q: Let y 5x? + 5x + 2. || Find the differential dy when x = 5 and dx = 0.3 Find the differential dy…

A: GIVEN: y = 5x2 + 5x + 2

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Given: y=ln9-x2 To find the differential dy

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 8x2 – 2 dy =

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Q: Find the differential dy of the given function.

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Q: Let y=5x2y=5x2.Find the change in y, Δy when x=3 and Δx=0.2   Find the differential dy when x=3 and…

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Q: Use the differential dy to approximate Ay when x changes from x = -3 tox = -2.99. y = x2 + 1 Enter…

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Q: Use the appropriate form of the chain rule to find the derivatives. 7x2 + 7y? + z²; x = psin ø cos…

A: This question is based on Partial derivatives.

Q: Find the differential d4y of the function y=x4.

A: Given function is

Q: H.W3:- Estimate y(0.2) ,using Euler method with step size h=0.1 where y':= -y°cosx „y(0)=1

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 7x2 − 3 dy =

A: Given y=7x2-3 Differentiating both sides: dy=14xdx

Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 8Vx + dy

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Q: 9. Find dy for y defined implicitly. by the equation xy-secly)-3x

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Q: Let y = tan(3x + 6). Find the differential dy when x = 2 and dæ 0.2 Find the differential dy when x…

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Q: ら)1f u-L -*9 sin (2x ty), x = s? + 2t" and y= 2s -t" au using at find the chain rule Ond as

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Q: when

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Q: Find the differential dy of the given function. y = sec2x/(x2 + 1)

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Q: Let y = tan(3x + 7). Find the differential dy when a = 4 and dæ = 0.3 Find the differential dy when…

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Q: Find the differential dy of the given function. y = Invs - x dy =

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Q: Find the differential dy. y = cubic root of 3x^2

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Q: Find the differential dy of the given function. y = V9 - x dy

A: Given y= √(9-x2) To find dy/dx

Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: Find the differential dy for y = x2 - 4x + 6, then evaluate it when x = 2 and dx = 0.1

A: Differentiate the given curve y=x2-4x+6 w.r.t.  x use the power rule of differentiation i.e.…

Q: Hello! Can you help me with this calculus problem?

A: Write y using exponent Then differentiate both sides. Use power rule and chain rule on the right…

Q: Let y = tan(4r + 4). Find the differential dy when x = 1 and dæ 0.4 Find the differential dy when x…

A: Given that, y=tan4x+4 differentiating both sides with respect to x, we get…

Q: tion of the separable equation dy 23 3 +2)³ + 2)?

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = xV9 - x2

A: Use  the differential of the form f = u.v

Q: Find the differential dy of the given function. Y=x+1/3x-2 Dy=?

A: Given, y=x+13x-2

Q: Find the differential dy of the given function. Xx + 5 y = 2х — 9

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Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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Q: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 9Vx+ dy =

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Q: Let y = tan(3x + 8). Find the differential dy when x = 3 and dæ = 0.1 Find the differential dy when…

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Q: Find the differential dy of the given function. Y= square root 7- x^2 Dy=

A: To find the differential dy of the given function

Q: Let y = tan(3x + 5). Find the differential dy when a = 4 and dæ = 0.1 Find the differential dy when…

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Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as:

Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.

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.