(b) Construct the Green's function of the problem: y" +y' - 2y r(x), 0Sxs1 %3D y(0) = y'(1) = 0 %3D and hence solve the boundary value problem for r(x) = 1.

Q: y" + y = sin x %3D

A:

Q: Find y' and y". y - In(x + VB+ x²) / 8 + x² 1 y' = V 8 +x2 y" II

A: Given: y=lnx+8+x2

Q: In a high school graduation class, (x,y) is in the relation r if person x is the same height as…

A:

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

A:

Q: ' (x² +2)+4x(y² +2y+1)=0, y(0) =1.

A:

Q: consider y'=-2y,y(0)=1 and analytic solution is y(x)=e^-2x a.Approximate y(0.1) using two steps of…

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Q: y" +y = 3 et/2) y(0) = 4 y(0) = 3

A: Second order non Homogeneous differential equation

Q: Eliminate the constant: y=x+c₁₂e¹+c₁₂e\ 1 Oy"-y=-x Oy"-y'+y=0 Oy"-y'=x Oy"-y=0

A: Given: The given equation y=x+c1ex+c2e-x To find: we need to eliminate the arbitrary constant.

Q: Graph without calculating the solutions/values y" + y' + 4y = &1(t), y(0) = 3, y'(0) = 0.

A:

Q: find y(x) for x2y'-2xy=3x with y(1)=3

A: Given,         x2y'-2xy=3x  with y(1)=3

Q: 2) (x² – 1)y' + 2y = (x + 1)²

A: Solve the following

Q: (1 – x)y" + 2xy' = 0 , y1

A:

Q: (t+2)y"-y'-(4t+10)y=0 Given y1=e-2t Find y2?

A:

Q: Show that the function f(1) = 5e²' satisfies y" – 3y' + 2y = 0, y(0) = 5, y'(0) = 10. %3D

A: The function ft=5e2t &amp; the differential equation y''-3y'+2y=0 &amp; the conditions y0=5,…

Q: x < 3x + 4 and 4x − 1 ≥ 15. Give your answer in interval notation, and sketch a graph of this…

A: Provided that                                       x&lt; 3x+4      and   4x-1 ≥ 15Take…

Q: Find the solution of y" – 2y' + y = 36 et with y(0) 6 and y' (0) = 5.

A: Given

Q: +4x 6) y' = Ans.: y-x =e +C. 3y - 2xye"

A: According to the guidelines in case of multiple questions we are only allowed to do first question,…

Q: Find all the second partial derivatives of the function a) f(x,y) = x* – 3x²y³. %3D | b) f(x,y) =…

A:

Q: 2. 3y² dy/dx-1=3x²+6ydy/dx, y(0) -1 and determine the interval of x in which the solution is…

A: To solve the given initial value problem:  3y2dxdy​−1=3x2+6ydxdy​ with the initial condition y(0) =…

Q: (x+y )dx+(x-xy)dy 0

A:

Q: a) Find a function f such that f'(x) = 4x2 – 2x – 1 and f(-1) = 2 %3D 2x b) Find the function g such…

A:

Q: Find y(x) y"-6y'+8y= 0

A: To Find y(x)

Q: x2y" + xy'+ y = 2x

A: The differential equation is x2y''+xy'+y=2x. The equation is in the form of a second order Euler non…

Q: (x’y* + 2x²y– y²)+(x*y³ – 2x³)y'= 0 when x = 1, y = 1 %3D

A: We will find out the required solution.

Q: (4) Find y' if y = xcot-12x -V1– 4x².

A:

Q: (1-x2)(dy/dx) – xy =1 homogeneous equation by linear equation method

A:

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: Solve simultaneously 2' (t) – 1 = y (t) – a(t) y' (t) = z' (t) – c/(t) æ (t) + z (t) = 1- y/(t)…

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Q: xy y' = x² + y² %3D with y(1) = -4, then y(e)

A:

Q: 1. y' = 2x x y. 4 x {y=4+ 6x3 C-X 3

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Q: y2+x2 5- y' %3D y(1) = -2 xy

A:

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.