Consider the initial value problem (IVP): dy 4x +3z2y? + 2x y- = 0, y(1) = -1. dx (a) Solve the initial value problem. (b) Give the largest interval over which the solution of the (IVP) is defined.

Q: Q3/ Solve the following equations: 1- х(2у — 3)dx + (x2 + 1)dy %3D0 dy 2- dx 4y x (у-3) 3. y' = 2xy…

A: Note that there are so many ways to write the final answer of the differential equation.

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Q: y' = [ 2 2 -1 2 y, y(0) = 8 [-]

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Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

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A: The given ordinary differential equation can be written as:

Q: (0-2) dy do With initial value problem // (0) = -1 - 2X - = 3 (8-2) seco tano

A:

Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

A: Given: A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is…

Q: f'(x) = z - 4r+ 12z + 12 and f(0) = 7.

A: f'x=x15-4x3+12x+12  &  f0=7 Integrating on both sides with respect to x, we get ∫f'x…

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A: Explained below

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A: Given differential equation is                                           dydx+yP(x)=ynQ(x);  x=y1-n…

Q: 6z dy (78)a

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Q: the st sub: Z = the + 4x = x²(4t + 3), x(1) = 4.

A: Given differential equationAssume

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A: The given differential equation is 2x+y+4dx+x-2y-2dy=0......(1) We shall solve the differential…

Q: 3) Debermine the explicib solution to tha Initral valve Prablem ylo1= 2 %3D

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Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: (b) Solve 1 y +-y= 0, t> 0. t

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Q: In(-/-) (vi) 2x In - x = 0

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Q: y' +y = x*y2 , y(2) = -1,x > 0 is

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Q: Find the general solution of the D.E. (y^2 - 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

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Q: Solve ylk + 2) + 2yjk + 1} + v[k] = 0 if y[-1] = 1, y[–2] = 1 %3D

A: Given,                            y[k+2]+2y[k+1]+y[k]=0                               ...(1)…

Q: Solve the initial value problem: (3x + 8)(y² + 4)dx – 4y(x² + 5x + 6)dy = 0, y(1) = 2

A: A differential equation is said to be in separable form if it can be written in the form . Such a…

Q: Find the general solution of x2y" - (2a-1)xy' + a²y = xa+1 where a is a constant.

A: Given  x2y'' - 2a - 1xy + a2y = xa+1  ----------(1)           This is Cauchy's homogeneous…

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Q: Solve y"-2y"-5y'+6y=0 general solution y(x) =

A: solution of the given problem is below...

Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

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A: According to guidelines we can do only first question thank you.We have to solve differential…

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Q: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

Q: (1 + t2)(dy/dt) + t · y = (1 + t2)5/2. Find general solution. SHOW ALL STEPS PLEASE. I DON'T KNOW…

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Q: Solve dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…

Q: Find general solution y = Yc + Yp of y(3) + y" 3e" + 4x2

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Q: 16xydx- 24ydy = -8x²dy %3D

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A: Given: y+2y=x

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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.