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Differential Equations
solve the second order differential equation
y" - 3y' + 2y = 3e^(-x) - 10cos3x y(0) = 1, y'(0) =2
y" - 3y' + 2y = 3e^(-x) - 10cos3x y(0) = 1, y'(0) =2
Differential Equations
solve the equation G (d^2)y/dx^2 - W(1-x)=0 where G and W are constants, subject to the conditions that y(0)=0 , y'(0)=1
Differential Equations
Solve the initial value problem by using laplace tranformation.
y"-6y' +15y= 2sin3t y(0)=-1, y'(0)=-4
y"-6y' +15y= 2sin3t y(0)=-1, y'(0)=-4
Differential Equations
If w= f{ xy/(x^2 + y^2) } show that x.∂w/∂x + y.∂w/∂y = 0
Differential Equations
If w=f S{xy/( x^2+y^2) } show that x.∂w/∂x + y.∂w/∂y =0
Differential Equations
If w = sin(x+kt) + cos(2x+2kt).
Prove that ∂^2 w/∂t^2 = (k^2).∂^2 w/∂x^2
Prove that ∂^2 w/∂t^2 = (k^2).∂^2 w/∂x^2
Differential Equations
solve the second order differential equation
y" - 3y' + 2y = 3e^(-x) - 10cos3x y(0) = 1 y'(0) =2
y" - 3y' + 2y = 3e^(-x) - 10cos3x y(0) = 1 y'(0) =2
Differential Equations
One of the standard experimental tests used in the study of fluid motion through porous materials consists of determining the displacement u when the material is given a constant load. The governing differential equation in this case is:
H[1+(du/dx)^3]*d^2u/dx^2=du/dt
Boundary Conditions: du/dx = -1 at x=0 and u=0 as x --> infinite
Initial Condition: u=0 at t=0
a) What are the dimensions of the constant H?
b) Find the dimensionally reduced form for the solution and then use this to transform the above diffusion problem into one involving a nonlinear ordinary differential equation. Make sure to state what happens to the boundary and initial conditions. You do not need to solve this problem.
H[1+(du/dx)^3]*d^2u/dx^2=du/dt
Boundary Conditions: du/dx = -1 at x=0 and u=0 as x --> infinite
Initial Condition: u=0 at t=0
a) What are the dimensions of the constant H?
b) Find the dimensionally reduced form for the solution and then use this to transform the above diffusion problem into one involving a nonlinear ordinary differential equation. Make sure to state what happens to the boundary and initial conditions. You do not need to solve this problem.
Differential Equations
the function k(x,y)=e^(-y^2)cos(2x) has a critical point at (0,0). What is the value of D at this critical point?
Differential Equations
Find the solution of the equation div(grad z)(x,y)=(e^(-x))cosy which tends to zero as x tends to infinity.
