Solve the given differential equation by undetermined coefficients. y" – 9y = (x2 – 2) sin(3x) eir + C2e rcos(3x) – r'sin( 3x) + sin (3x) -3x : cos( 3x) 1 y(x) = (c, e3x 12. x´sin(3x) + -sin(3x) 81 27 18

Q: Q1) solve the following differential equation 2- 3- y² (cos x +)dx + (e² + 2yIn(x))dy = 0 (sin³ (x)…

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Q: Solve the exact differential equation: (2y sin x cos x – y + 2y?e*y)dx = (x – sin? x – 4xye*y')dy

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Q: Find the general solution of the differential equation: d²y + 36y = 0. dx? y = C1 sin 6x +C2 cos 6x…

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Q: Form the differential equation by eliminating the constant 'a' from r=2a (sin 0- cos 0)

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Q: Solve the differential equation. dy y + 1 dx O In |x| – ? () = tan - ex - x + tan-'(x) = C In |x| –…

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Q: Consider the following differential equation to be solved by variation of parameters. y" + y = sec…

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Q: sec y Obtain the solution of the differential equation y' x-4x+5 a. 2 sin y = In(x² – 4x + 5) + C b.…

A: ∫cosx=sinx +c∫dx1+x2=tan-1(x)+cCosx=1secx Given D.E y'=sec(y)/x^2-4x+5

Q: 1. Find a particular solution of the differential equation. Do not solve the full equation. (a) y" |…

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Q: Evaluate the given differential equation cosy sin2x dx + ( cos²y – cos x)dy = 0 A. cos x (1+ siny) =…

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Q: consider the differential equation dy/dx=sin(x)/y for which the solution is y=f(x). Let f(0) = 1…

A: Given dydx=sinxy, y0=1. By variables separation,  y dy=sinx dx Integrating on both sides,

Q: werty that the indicated function() explicit solution of the given first-order differential 2y² = y²…

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Q: y = G, cos 3x – C, sin(-3x)

A: The general solution of a differential equation is y = c1cos(3x) - c2sin(-3x) We need to find the…

Q: nd the solution of the differential equation = Z 3 + sin(z) with i dz

A: Given: dfdz=z-23+sin(z)f(0)=2

Q: Solve the given differential equation by undetermined coefficients. y" + y = 5x sin(x) 5.2 -x cos x…

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Q: Solve the following differential equation y' (x) = y· cos(x) O y (x) = sin(x) + C O y (x) CeCos(z) O…

A: Topic - solutuon of differential equation

Q: 2. (2.xy – sin x)dx + ( - cos y dy = 0

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Q: Solve the following differential equation by using Inverse Operator method…

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Q: (2y sin(x) cos(x) – y + 2y e) dx = (x – sin (x) – 4xyey)dy.

A: the differential equation Mdx+Ndy=0 is exact when ∂M∂y=∂N∂x where M and N are functions of x and y…

Q: 2 1) Solve : (D² − 6D+9]y = x²e³x cos2x -) Solve : (x² D² − xD + 4)y = cos log x + x sinlog x :)…

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

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.