Differential Equations Answers

use the laplace transform method to solve the boundary value problem

∂u/∂t=3(∂u/∂x), u(x,0)=4e^-2x

Use the method of separation of variables to determine the general solution to the one dimensional heat equation ∂²u/∂x²=1/α(∂u/∂t),0≤ x≤ l,t≥0 subject to the boundary conditions u(0,t)=u((l,t)=0 and the initial condition u(x,0)=f(x). Determine the particular solution when f(x)=x²

Determine the laplace transform for ∂u/∂t and ∂u/∂x. Hence using the laplace transform method, solve the partial differential equation ∂u/∂t=u-∂u/∂x. subject to the initial condition u(x,0)=e^-7x,x>0,t>0

Apply the method of Varition of parameter

d^2y/dx^2 -4 dy/dx +3 y = 1/1+e^-x

Solve the method of undermined coefficient (D^2+8D+16)y=8e^-2x ; y(0)= 2 y'(0)= 0

what is the separable variable? dy/dx = y² sin x², y(-2) = 1/3?

y' = csc x - y cot x

(3xy+3y-4)dx+(x+1)^2dy=0