1) x’y"+xy'-y=x²+1,x>0 however, the differential equation is given a) One of the linear independent solutions of the homogeneous part of the given differential equatio Y =x other linear independent y2-month y,(x)= y;(x)| - *dx Formula find usin solution b) xy"+xy'-y=0 create the basic solution sentence of homogeneous equation and write the solution c) xy"+ xy'-y =x² +1,x>0 equation (by lowering the order) write down the general solution by downseing it from the order to the differential equation

Q: Let Find A-¹ and use it to solve where where x₁ = -24 and 2 -0 = A = 4 -3 4 4 AX = B B = (²3) X = -…

A: We see,        So, Determinant of A = |A| = 4×4 - (-3)×4                                        = 16…

Q: 1. Use the Wronksian to verify the given functions form a fundamental set of solutions of the…

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Q: : Solve the differential equation a) (3x2+ycosx)dx+(sinx-4y3)dy=0 Hint exact equation b)…

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Q: 3 Solue Cy+2*g³)dx + C2+3x' (2+ 3x*;'+ x) dy=0

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Q: verify that the function. solution to the differential and find the y=c₁e-x + C₂ e 2x is a equation:…

A: Topic = Differential equation

Q: 2. Solve the initial value problem z""+x" - 4x' - 4x = 0, x(0) = 1, x'(0) = 0, x" (0) = -1. Hint:…

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Q: solve A) y''-2y'=6e^2x-4sin(x)

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: The general solution for the equation y'=x*e(x^2+y) can be given in the form of: ?ex^2+2e-y=k a) x…

A: Solve by separable variable method

Q: Solve using De Moivre's Theorem to find the general solution.  y^(8) + 8y^(4) +16y=0

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Q: Question 5 > Find a particular solution to the equation using variation of parameters. y'' – 10y' +…

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Q: Problem 2: Pure-time differential equation} \ Consider the following equation d 3t e de (t). +…

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Q: Solve y" - 2y" - y' + 2y = 0. Include a plot of the solution curves.

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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.