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Differential Equations
By changing the independent variable.solve the differential equation. d2x/dx2 - (dy/dx)(1/x) + 4x2y = x4
Differential Equations
Find the solution of the initial value problem y′′+4y=t^2+6e^t, y(0)=0, y′(0)=5.
Enter an exact answer.
Enclose arguments of functions in parentheses. For example, sin(2x).
Enter an exact answer.
Enclose arguments of functions in parentheses. For example, sin(2x).
Differential Equations
(2D^3+3D^2D'+4DD'^2+5D'^3)z=x^2+y
Differential Equations
Solve (y-z/yz)p+(z-x/xy)q=x-y/yx
Differential Equations
solve(D^2+2DD'+D'^2)z = e^x+2y + sinh(x+y)
Differential Equations
cos^2ydx+(1+e^-x)sinydy=0
Differential Equations
D3-3D²D'+ D'³ z= 0
Differential Equations
Use the method of variation of parameters to determine the general solution of the given differential equation.
y′′′−y′=5t
Use C1, C2, C3, ... for the constants of integration.
y(t) = _______
y′′′−y′=5t
Use C1, C2, C3, ... for the constants of integration.
y(t) = _______
Differential Equations
1. Find the general solution of the differential equation.
y′′′−6y′′−36y′+216y=0. Use C1, C2, C3, ... for the constants of integration.
y(t) = _______
2. Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used.
Do not evaluate the constants.
y′′′−4y′ = te^−2t + 3cos(2t)
Use J,K,L,M as coefficients. Enclose arguments of functions in parentheses. For example, sin(2x). Do not simplify trigonometric functions of nt, where n is a positive integer.
y′′′−6y′′−36y′+216y=0. Use C1, C2, C3, ... for the constants of integration.
y(t) = _______
2. Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used.
Do not evaluate the constants.
y′′′−4y′ = te^−2t + 3cos(2t)
Use J,K,L,M as coefficients. Enclose arguments of functions in parentheses. For example, sin(2x). Do not simplify trigonometric functions of nt, where n is a positive integer.
Differential Equations
1. A mass weighing 8 lb.stretches a spring 3 inches. The mass is attached to a viscous damper with a damping constant of 2 lb - s/ ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s , find its position u at any time t . Assume the acceleration of gravity g = 32 ft/s.
