Consider the following ODE d^2y/dx^2+x^2dy/dx-cos(x)y=y-2xy With initial conditions: y(0)=3 and y'(0)=1 a) Convert this ODE to a set of first order ODEs

Q: Determine the phase shift of the function y = sin(x - π/3)

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Q: dr/dθ= cos (-5πθ), r(0)=9

A: Given,

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: y = 2 sin (20+ 4π 3 ^

A: Given query is to find phase shift.

Q: Find dy/dx for x*+siny = x'y

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Q: Integrate the following functions [(-2x² – 9x – 7)dx [(4x° – 9)* (20x“ )dx. i. ii. ji.

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Q: Integrate (sin1/2)(x)dx

A: The given integral is ,∫sin12x dx=∫sinx2  dx

Q: y = 2 sin 3x 1+3 cos2x

A:

Q: Find y' and y". y=2sin4x-cos(8x-1)

A: Let's find.

Q: find y'. (show all the steps please) cos(xy) = x-y^2

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Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

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Q: y′= (6xe^(6x)) X (cos^(2) (6y)) a) Write the equation in an integrable form by separating it into…

A: Solve using variable separable method.

Q: find dy/dxy=x/1+cosx

A: we have to find derivative of f(x)we will use following rule

Q: Solve: (1+y2)dx=(tan-1y-x)dy

A: Here we have (1+y2) dx = (tan-1y-x) dy We know that solution of the differential equation in the…

Q: Find dy clx In (sin(8x3)) a) y=(√√x2-1) In (sin( b) y = 1+ sin ² (3x)+sin 4 (3x) + sin 6 (3x)+.... +…

A: Since, you have posted multiple questions.As per guidelines we are supposed to answer only first…

Q: [3-v5 (2v7 dx sin(2x)

A: According to the definition, if dFdx=f(x), then ∫f(x)dx=F(x). The function f(x) is called the…

Q: 2x – sin y y' = x cos y

A:

Q: SOLVE THE FOLLOWING ODE STEP BY STEP IN DIGITAL FORMAT PLEASE 4y = (y')² - 4 xy' + 2y = sin y

A: Since you have asked multiple questions here, we will solve the first one for you. To get the…

Q: Find y'. sin t y = 8 + t %3D y' = %3D Find y'. 2 sin 0 + 9 cos 0 y = %3D sin 0 – cos 0 y' = %3D

A:

Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

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Q: dx

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Q: Find dy y= cof ( + tan)

A: Given : y = cot-12x+tan-1x2

Q: y = (cos x-x4+ 1/x2)5 - In (3x+1)  Find dy/dx

A: =?

Q: у%3D sin(4x — 2) cos (4x + 2) || -

A: topic - derivative

Q: 1- 2- If x=y√√1-y², find Find y' for y=cos(sin²x) dy dx

A:

Q: -2 ' = cot (sinx') 3 3 Find (y') xsec x %3B

A: Given, y=cotsinx3

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.