Differential Equations Answers

1) Find the half range Fourier cosine and sine series for

𝑓(𝑤) = 1 − 𝑤; 0 < 𝑤 < 1

Reduce the equation Zxx - (1+y)² Zyy = 0 to canonical form

(D+3)^2y=sinh2x

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution x^3 (y''') + 6x^2 (y'') + 4xy' - 4y =0; x, x^-2, x^-2 (lnx), (0,infinity)?

Solve yzdx-xzdy-(x^2+y^2)tan^-1(y/x)dz=0

Hermite’s differential equation is

d2y/dx2 - 2xdy/dx+ 2py = 0;

where p is a parameter. This equation is very useful for treating the simple harmonic oscillator in

quantum mechanics. Find the series solution

Using power series method to solve the initial value problem

(x − )1 y′′ + yx ′ + y = 0 , y )0( = 2 , y′ )0( = −1 .

1.Solve Cos y cos px + sin y sin px = p

2.Solve

(D^3+2D^2+D)y= e^2x + x^2 + sin2x

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