Use Euler's method to numerically integrate dy -2x3 + 12x2 – 20x + 8.5 %3D dx from x = 0 to x = 0.5 with a step size of 0.5. The initial condition at x = 0 is y = 1.

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A: The given differential equation is  y2+xy3dx+5y2-xy+y3sinydy=0

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Q: Find the particular solution, Using the integrating factor method: dy + In x =- dx y where y(1) =3.

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Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

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Q: Find the Particular Integral for the given differential equation d²y dx2 dy +3 +6y =2x+ 15 dx (10…

A: 1

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Q: dx 2. dt x(0.5) = 1, solve for x(1) when h = 0.1 2(t+1)

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Q: 2. Use the 4th-order Runge-Kutta method to integrate dx = t - sinx dt given x(0) = 1, using a step…

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Q: With the aid of an appropriate integrating factor, calculate the initial value of the equation…

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Q: dy Find y(0-2) by using Euler's method for y=1 for x= 0. log10 (x+y) with initial condition %3D dx

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Q: Find the integrating factor: dy 3y = x (1 + x?) dx e3x None of these e-3x x3

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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.