Use 3rd order Runge-Kutta approach to solve for the following ODE for the interval [2 6] using a step size of 2. It is given that y(2) =-2. Provide also an analytical solution and compare your numerical-solution-based results with the analytical solution. dy 4 + 4x2 = x³ – 8 dx

Q: Differentiate. y= In [(x +2)° (x + 5 (x+ 7)°] [In [x+ 2)° (x +5)*(x + 7) ]] =O dx

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Q: Which of the following functions is a solution of the exact equation? (6x + 4y)dx + 4xdy= 0.

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Q: xp z/1 (1 − 1-x7)x^ S 4.

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Q: SOLVE FOR CL is constant : A² jª (a²-2₁²x² + x²) dx = 1

A: The given integral is A2∫-aaa4-2a2x2+x4dx=1. We have to find the value of a.

Q: Differentiate the function. y= (5x- 1) (1-x°) dy %3D dx

A: Given that the function is      y = (5x-1)2(1-x3)4

Q: 3/41 x² 3/5 √2x³-1 dx.

A: Consider

Q: 24 - dx /3- 4x (х + 1) 3.

A: Given that:

Q: Ho Find (yor dy d'y ) and (y or -) for the following functions: dx dx L 2. y= x² (x-1)² 5. y=(x²…

A: We need to find the first order and 2nd order derivatives of the given functions.

Q: Find 3 J (æ+ 1)/2x² + 4x + 6 dx. OTM

A: We have to find the integral of the given function.

Q: Find the values of d/dx (11) and d/dx(π)

A: Consider the provided information, ddx11   and   ddxπ. Find the values of the derivative. The…

Q: y = √sin(7x + In(5x))

A: We know that the derivative of x^n=nx^(n-1) So derivative of sqrtx=1/(2sqrtx)

Q: Y(3x*2)dx + x (1-2y) dy-0

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Q: Solve the following ODE * (y+x*y²) dx+x dy = 0

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Q: Solve this intial value problem using the Laplace transform: y''+3y'+2y = 4t if 01; y(0) = 0, y'(0)…

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Q: Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

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Q: x2 dx = 17. x+1 18.The first step in calculating | dx is: (2x -4)(x+3)²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 27. y = 2e*√√x

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Q: y 1+lnx+ dy Solve dx 1-lnx

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Q: Differentiate the function. y = (4x-11)2

A: Chain Rule of differentiation : dydx=dydu·dudx

Q: a. (In(x² − 3x + 1)) = = b. — (In(ex + 5x)) = d a + (n (+)) = [ C. dx +1 Hint: Use properties of…

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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.