(1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: (xy2 + x- 2y+3)dx + x2ydy 2(x+ y)dy 4.

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Q: Determine if the equation (dfferential form) is exact and find the solution if it is…

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Q: Find Df, Rf : Y= 3/(2x+1)

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Q: xsin ax 2 2 (x²-x²) 1/2 Show that [²= - dx - TV J₁ (ay) 2

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Q: C=X+Xyz for y

A: Given,           w = x + xyz

Q: Function dy du dy du dx dx = (5x³ – 7x² + 2x – 3)*) _y = csc(x² – 3) y = 5x² – . y = V5x2 – 4 _y =…

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Q: dx 1-S 1-sinx

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Evaluate -42 (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) X

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Q: let r (t) = The y component of r' (5)

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: Differentiate these using the product rule. Write your answers in fully factorised form with the…

A: NOTE According to our guidelines we are supposed to answer only one question and three subparts.…

Q: Evaluate [1+(x- 1)2 +4y²]dydx

A: Given: The given integral is ∫03∫021+x-12+4y2dydx. Integrate the integral with respect to y.…

Q: Find Joy²dx + (xy-x²) dy along C: y = 7x from (0,0) to (1, 7).

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Q: E- Use the chain rule to express dy / dx in terms of x and y: a) y=7+1 and t=2x+1 1 b) y=7+1 and x=…

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Q: Find // (5x + y)dA where D : {(x, y) | x² + y? 0}

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Q: Find // (4x + 2y)dA where D = {(x, y) | a² + y? 0}

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Q: Find y in terms of x. dy aY = x 4(x 5 - 3) 2, curve passes through (1, 5) dx 17 (A y = (x5- 3) 3 +…

A: Consider a given differential equation isdydx=x4x5-32.The curve passes through the point 1,5.Express…

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.