Differential Equations Answers

A string is stretched and fastened to two points  apart. Motion is started by displacing the string in the form  from which it is released at a time , the initial velocity is zero. To find the deflection

Identify the level curves of the following functions:

(i) √(x²+y²)

(ii) √(4 - x² + y²)

(iii) x-y

(iv) x/y

(D⁴ - 64) y= x cos x

use the method of diagonalization to obtain the general solution of the given system of differential equation d^2x1/dt^2 =5x1+4x2 and d^2x2/dt^2=x1+2x2

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1)Find the general solution to the equation (cos y + 2) dy/dx = 2x.

(D -2) x + Dy = 10sin2t

Dx + (D+2)y =0

(D+3)^2y=sinh2x

Find general solution of the differential equation

dy/dx=y²(1+e^x)

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Find the particular solution of dy/dx = ycosx/1+2y^2 given y(x) = 1; y (0) = 1

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1)Find the general solution of xdx = 9x^2x -ydy