d²u np + xu = 1 dz Q3. Given dx² du(r 0) = 1. 2 u(x=0) = 1, 0

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…

Q: Solve the diff eq. (Homogenous) dy dx + x²(y² + 3) y(x³ + 1)

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Q: Use three steps of Euler's method to obtain an approximate solution of: dy = dx 4* y subject to the…

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Q: Use the Euler's Method to approximate the solution of the equation. Complete the table. dy dx x+2y²,…

A: Given y′=x+2y2, y(0)=2, Δx=0.05,  n= 5 so we have to find y(0.25)Euler methodyn=yn−1+Δxf(xn−1,yn−1)

Q: Use Euler's method with h = 1/4 to compute approximate values of y(1) for t.y'= y(sint), y(0)=2.

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Q: Given that y = x is a solution of ď²y (x²(5 + x²)). dx² (15x) dy + (15)y=0, in x > 0, find another…

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Q: dy| 2х — 6 - Find- , where y = dx\x=1 x + 2 Enter the exact answer. dy dx=1

A: Solve

Q: I need help with solving number 4

A: Refer to the question, we need to find the third derivative of the provided function.

Q: Use Euler's modified formula to find an approximate value of y whenx = 0.3, given that = x+y and…

A: Given  dy/dx = x+y and y(0)=1 To determine y(0.3) using Euler's modified formula

Q: Given h = 0.1. Solve using fourth-order Runge-Kutta method: 2 tây=0;(0)=39;y/(0) 3. Find y(0.1) and…

A: Given differential equation is d2ydx2 -2xdydx +8y =0 Initial conditions:- y0=39; y'0=3 step size:-…

Q: yes, hi. I've seen another source, use set variables to 0 and then solve individually, answers are…

A: setting z=0 and solving for x and y. similarly setting y=0 and solving for x and z.

Q: 1 Selving ou au at

A: We solve it by seperation of variable method.

Q: Solve the following IVP. You may leave your answer implicit in y. dy = 0, (2.x+y³ sec² (x)+ (1+ 3y²…

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Q: b) d² y dx² +4y= cos 2x, y(0) = 2, y'(0) = 4

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Q: u" (x) = – sin(x), 0 < x < T, u(0) = u(7) = 0.

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Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

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Q: Solve the Euler equation d²y dy 3x? dx -5у%3D0 +x dx given that y(1) =1 and y'(1) = 2.

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Q: dy For = 2x +y and y(0) = 2, use Euler's method with h=0.1 to approximate y(0.5). dx Approximating…

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Q: e.Find the solution of equation (29) by replacing v by y/x  dy/dx =( y − 4 x)/( x − y) .

A: Given differential equation is dydx=y-4xx-y Given equation is homogeneous differential equation.…

Q: dy Solve dx = xy using Runge-Kutta method for x = 0-2 given that v (0) I taking %3D h = 0-2.

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Q: If so be solvet using atgebrate 3/2 /2 Substitufion, give the substitution for X and dx.

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Q: dy For = 4x/7+ y? and y(0) = 2, use Euler's method with h = 0.1 to approximate y(0.5). dx…

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Q: dy Find the solution of the Bernoulli's equation x + 6y = 3xy4/3. dx 1 1 а. у b. y (x2+cx)3 (x+c)3 1…

A: We solve by Bernoulli's equation.

Q: b) Solve by direct integration: er dy dx dy 8 given y-5, when x=0

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.