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 ∂ ^2u/∂t^2 = c^2∂ ^2u/∂ x^2

P^2x+q^2y-z=0

If y=2x + Ce^x is a solution of the differential equation dy/dx-y =2 (1-x) then find the particular solution satisfied by x=0, y=3

Integral of 1/√(3x^2-6x+2)dx

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

Show that, for the differential equation d^2y/dx^2 + a(x)dy/dX + b(x)y=0, e^(mx) is a particular integral if m^2+am+b=0. Hence find the value of m so that e^(mx) is a particular integral of the equation (x-2)d^2y/dx^2-(4x-7)dy/dX + (4x-6)y=0.

Solve the following ordinary differential equation:
{y(1+(1/x))+cosy}dx +(x+logx-xsiny)dy=0

p^2+q^2-2px-2qy+2xy by charpit's method find the complete integral this differential equation

Consider the differential equation
x^3y ''' + 10x^2y '' + 16xy ' − 16y = 0; x, x^−4, x^−4 ln(x), (0, ∞).
Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.
The functions satisfy the differential equation and are linearly independent since
W(x, x^−4, x^−4 ln(x)) =
≠ 0
for
0 < x < ∞.

Form the general solution.
y =


Could someone help me i´ve been on this one for hours I don´t know how to do it and my assignment is due in about an 1 and a half