Differential Equations Answers

Solve :

P² -2xyp + 4y²=0, where p=dy/dx

Using the method of variation of parameters, solve the equation:

d²y/dx² +a²y = sec ax.

Solve:

x²y²(2ydx + xdy) - (5ydx + 7xdy) =0

If f(x, y) ={ 1 if x=0 or y=0 and 0 , otherwise } then lim f(x, y) does not exist for limit (x, y) approaches to (0, 0).

Solve the problem of the vibrating string for the following boundary conditions

1. y(0,t)= 0

2. y(l,t)= 0

3. dy/dt(x,0)= v0 sin nπx/l

4. y(x,0)= y0 sin 2πx/l

 Show that the equation 𝑦 = 𝑥𝑒 𝑥 is a solution of the differential equation: 𝑦 ′ − 𝑦 − 𝑒 𝑥 = 0

y'=cos(x+y)

The function f(x, y) =cos √x^3 +y^3 is a homogenous function. Say true or false.

Solve for the general solution using method of undetermined coefficients D4-1y=e-x

using D' Alembert method, find the deflection of a vibrating string of unit length having fixed ends, with initial velocity zero and initial deflection f(x)=asin²nx