Find the solution of the differential equation d'o/dx + p + x = 0; 0 < = x < =1 subject to the boundary conditions (0) = ¤(1)=0, usir point collocation method. [Use C;x(x-1) + Cx'(x-1) as the trial function with x=1/3 and x=3/4 as collocation points].

Q: Q1: Solve the following initial value problem (IVP). y' =2_2x³ X -sinx², y(√) = √ y

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Q: - y" – 2y" + y' = 2 – 24e* + 40e, y'(0) = }, y"(0) = - y(0) = ;, 9. 2

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Q: (x^2)y''-2xy'+2y=0; y(1)=4, y'(1)=7   Find particular solution that satisfies the given condition

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Q: y" – 2y' + y = -3 – x + x², y(0) = –2, y'(0) = 1. %3D %3D

A: Given: y''-2y'+y=-3-x+x2 ; y0=-2, y'0=1 So, We can also write as; D2-2D+1y=-3-x+x2   The auxiliary…

Q: Find the general solution of the given differential equation using variation of parameters. П y" +…

A: We have to find the general solution of the given differential equation using variation of…

Q: Obtain approximate value of y at x=1.5 for the differential equation: y'-2y+3ex, y(0)-1, using Runge…

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Q: Do you think that the initial-value problem y'=xy^(1/2), y(0)=0 has a unique solution? Justify your…

A: It has no unique solution.

Q: Use undetermined coefficients to find the particular solution to y''+ 8y' + 15Y = e 2"(13 + 12x) (13…

A: Consider y''+8y'+15y=e-2x(13+12x) To find the particular solution using method of undetermined…

Q: Solve the initial-value problem (-1, 00): on (2x + 3)y" – (2x + 5)y' + 2y = (2x + 3)?e2 y(0) = 0,…

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Q: Find the solution of the given initial value problem. y" + 2y' + 2y = cost + 8(1 - 5); y(0) = 5, y'…

A: We will find out the required solution.

Q: Note that y(t) = c1 + c2t + (t^(3) /6) is a general solution for y''= t. Find c1 and c2 such that…

A: Given equation is y''=t The general solution of the equation is given by  yt=C1+C2t+t36...........i…

Q: Consider the differential equation: (56x^2)y″−16x(x+7)y′+16(x+7)y=5x3, x&gt;0.   You can verify that…

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Q: What is the solution of y2 - x2y'=0 with IVP y(1)=1/2 ?

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Q: What is the solution to the IVP? y''+y'+4y=0      y(0)=1     y'(0)=-1

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Q: Find the solution of y' + p(x) = 4x if y(0) = 3 and where

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Q: Find the function with derivative f'(x) = e4x that passes through the point P = (0,5/4). f(x) =

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Q: Example: Determine and interval in which a solution to the IVP is guaranteed to exist without…

A: To Determine :-  The interval in which a solution to the IVP is guaranteed to exist without solving…

Q: Consider the differential equation with the initial condition that y=1 when x = 1. What is the…

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Q: Find the singular solution to the Clairaut equation y = xy' + In(-27 - y'). none y= 13 x +1 –…

A: General solution to the clairaut equationy=xy'+ln(-27-y')is given by y=cx+ln(c)Now, differentiate…

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

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Q: Consider the initial value problem x^2y'' + 3y = 2e^x subject to initial condition y(1) = 0. For…

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Q: Discretize the differential equation - 3ty=-2t, y(3) = -2 over the interval [2, 3] with step-size h…

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Q: Determine if the following initial value problem has a unique solution in some open interval around…

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Q: y" – y' = sin(t) y(0) = 1 y' (0) = -1

A: We have to solve the IVP           y''-y'=sinty0=1y'0=-1

Q: The function y = x2 In x is a solution to the differential equation 4x² y" + y = 0. First, use…

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Q: Solve the DE y' = xe2y, subject to the initial condition y(0) = -1. Oy = -(1/2) In (-x^2 - e^2) Oy =…

A: This differential equation can be solved by using the method of separation of variables.

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.