Differential Equations Answers

solve the heat conduction equation: 8*∂^2u(x,t) /∂x^2 = ∂u(x,t)/∂t; for0<x<5 and t>0 the following boundary and initial conditions: u(0,t) = u(5,t) = 0, u(x,0) = 2sin(πx) − 4sin(2πx)

Obtain the value of the constant c for which the function u(x,t) = cosαcxsinαt is a
solution of the wave equation . 2
2
2
2
2
x

Solve the following ODE using the power series method: (x^2-1) y′′ +3 xy′ + xy =0

Solve: y2(x-y)dx+x2(x-y)dy+z(x2+y2)dz=0

Solve the differential equation.
1. dy/dx=cot(y+x)-1
2. (x^2+y^2)dy/dx=xy.

2x(y+z^2)p+y(2y+z^2)q=z^2
And prove thatyz(z^2+2z-2y)=x^2

If y1 = 2x+2 and y2 = -x^2/2 are the solutions of the equation y= xy' +( y')^2/2 then are the constant multipliers c1 , c2 are arbitrary, also the solutions of the given D.E. ? Is the sum y1+ y2 a solution ? Justify your answer.

Find the general solution of the differential equation y^2/2+2ye^t+(y+e^t)dy/dt = 0

A mass m, free to move along a line is attracted towards a given point on the line with a force proportional to its distance from the given point . If the mass starts from rest at a distance s from the given. Show that the mass moves in a simple harmonic motion.

Solve the following ode using the power series method (x^2-y)d^2y/dx^2+3xdy/dx+xy=0