Let a and b be two positive constants and define the regular surface patch o(u, v) = (au, bv, u² + v²). 1. Find the standard unit normal to the surface patch o at the point o(a, b).

Q: 4. For y' = y3 +y² – 6y, Find the critical points. Draw a phase diagram and mark the critical points…

A: Given y'=y3+y2-6y Given a differential equation y'=fy a point y0 is said to be a critical point if…

Q: 3. (D3-2D2+D-2) y=0 4. (4D3+28D²+61D+37) y=0

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Q: 2. Find a homogeneous linear equation with real, constant coefficients that is satisfied by: y = 6 +…

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Q: Differential Equations homework.

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Q: 1. Solve y' = "ty´, with initial condition y(1) = -2. x2+ +y? xy

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Q: Ydx - xdy + x(2 - y)dy = y? ey dy %3D

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Q: a) Find a plane curve whose signed curvature is given by k,(s) where a is a positive constant and s>…

A: The given signed curvature is ks(s)=12as

Q: Find the general solution of the given system. X' x = (10_-5)x 8-12, X(t) =

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Q: let a=(2,4-3), 6=(60,1),c=(0,-1,5) eguation of line thoough ' parallel to % what é the @) Yhe 6) Khe…

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Q: Find the Laplace transform, F(s), of this function f(t) = e-2t t cos 3t

A: We use first shifting Theorem to find the Laplace transform of given function which states that  IF…

Q: 7. A 100-gal tank contains 40 gal of an alcohol-water solution 2 gal of which is alcohol. A solution…

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Q: Find the Wronskian of the functions f(t) = 6e' sin(t) and (t) = e' cos(t). NOTE: Your answer must be…

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Q: the plane according to the equations x = t² + 2t and y = 2t³ – 6t. Find dy/dx c. 3 d. 4

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Q: Find the derivative of the function described. (Rx5) 4х-2 5. у 3 3x+4

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Q: 13. Find the equation of the line with slope equal to 1 and normal to the curve x2 + 3xy +y? = 5 at…

A: GIVEN: curve is x2 + 3xy + y2 = 5

Q: Explain Bessel equation and Prove that 2 (n + 4)Jn+4x (i) (ii) In+3X + Jn+5X = 4J"n = Jn-2 – 2Jn +…

A: The objective is to explain Bessel equation and prove that  (i) Jn+3x+Jn+5x=2xn+4Jn+4x (ii)…

Q: 9. At what point(s) on the circle x 2 + y? = 13 is its tangent line parallel to the line 3x – 2y = 6

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Q: Find the general solution of the given equation. y" + 36y = 0 Choose the correct solution below. c,…

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Q: Differentiate log(x² + 1)² 4 log10 e а. x2+1 4x log10 e b. x2+1 a.

A: Given query is to find derivative of the expression.

Q: 3. x³y'= 2 (y*+x %3D

A: A detailed solution is given below

Q: Homogeneous Find C, if f(e) = 2 = y & e = 2.718281828 (y - xy)dx + x*dy = 0

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Q: Given the differential equation dy = 4x - 4y with initial condition that y(3) = 0.1. dx Use Euler's…

A: Answer given below in great details.

Q: 2 1 2. Solve the linear system i = Ax, where A 1

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Q: -x+Vx + y dy The Differential Equation dx describes the shape of a plane y curve C that will reflect…

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Q: Solve the following equation using method of undetermined coefficients. y() + y"= 3x² +4sin x -2 cos…

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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.