Solve the following initial value problems. Is the solution that you found unique on some interval? Justify. (a) dy = 2x²y², y(1) = −1.

Q: . Solve by using variation of parameters: y" – 10y' + 16y = 4e*

A: We have to solve the differential  equation  using variation of parameter.

Q: fy = e2" 2-3 , then find y" at x = 0 Enter your answer as a decimal

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Q: 5. Show that T = + y? satisfies the equation T + Tyy = T³

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Q: solve the following using variation of parameters: y"+9y=1/4csc3x

A: The given differential equation is y''+9y=14cosc 3xORy''+9y=sin 3x4 The solution using the method of…

Q: x - 2xy - 3y" : y(1)=; dx

A: The given equation is first order Bernoulli's ordinary differential equation. y'+p(x)y=q(x)yn The…

Q: Solve the following using variation of parameters show complete solution: 1. (D²3D + 2)y: = 2x 1+ex

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Q: dy 3. x. e*y. + y. e*y - 4x3 = 0 dx -

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Q: 3. A pomegranate is tossed upwards at a speed of 40 ft/sec. The pomegranate starts at 4.5 feet above…

A: Given,  Initial height = 4.5ft Initial speed = 40 ft/sec

Q: Help me fast so that I will give Upvote.

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Q: Solve for the value of C in the equation: dx 3y³ II (1-2x)dx 3 when y(0) = 1

A: The given differential equation dyy4+dx3y3=1-2x3dx We have to find the value C when y0=1

Q: IHA = ; . III. B X1 x2 And X = lx3 x4!' Solve each of the following equations: 1. (d) (B - I)x = IC…

A: It is given that A=1234,  B=3110 ,  C=1224. 1. (d).…

Q: (7y+yt/t)=n Solve for y

A: The given expression 7y+ytt=n Solving further 7y+y=n8y=ny=n8

Q: 1. Consider the function f(x) = 7x3 – 8x + 4. Find the solution of the equation f(x) = 0, within…

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Q: (6x + 1)y2 dy Solve: (6x + 1)y´Jr + 3.x² + 2y³ ||

A: An equation of the form  Mdx+Ndy=0 is said to be exact if  ∂N∂x=∂M∂y. To solve exact equation we…

Q: (c) Solve for each of the following. dx (i) Vĩ + Jỹ = 4 (ii) y = 2x2+1

A: We have to find the first derivative of given function.

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 - A. 1/4 B. 1/2 C. 3/4…

A: Find integration factor first as it is linear differential equation

Q: 1 y2 y3+3 dxdy 0 0

A: Let I=∫01∫0y2y3+3dxdy

Q: Solve and sketch the graph of the IVP. dy dt = 81 (1)-82(1) +83 (1)-84(1)+.... y(0) = 0

A: As per the question we are given the following IVP : differential equation(DE) : dy/dt = δ1(t) -…

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1

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Q: Given (x + 6y? ) dx - 4xdy = 0, when x = 1, y = 1. Find the particular solution.

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Q: (y² + xy) dx-x² dy = 0, when x = 1, y = 1

A: Given that the equation y2+xydx-x2dy=0. Find the particular solution of the given equation when…