Explain why the general solution of the Nonhomogeneous Second Order
Linear Equation (NHSLE) y''+ p(x)y' + q(x)y = f(x) has the form y =
y_h + y_p where y_p is a particular solution and y_h is a general
solution
find the general solution of the given differential
equation.
1. y'' + y = tan t, 0 < t < π/2
2. y'' + 4y' + 4y = t-2 e-2t , t >
0
find the solution of the given initial value problem.
3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1
1)Find the general solution of the given second-order
differential equation.
y'' − 7y' + 6y = 0
2)Solve the given differential equation by undetermined
coefficients.
y'' + 4y = 6 sin(2x)
Second order Differential equation:
Find the general solution to [ y'' + 6y' +8y = 3e^(-2x) + 2x ]
using annihilators method and undetermined coeficients.
4)Find the general solution of the following differential
equation.
y''+4y=tan(x) -pi
5)A mass of 100 grams stretches a spring 98 cm in equilibrium. A
dashpot attached to the spring supplies a damping force of 600
dynes for each cm/sec of speed. The mass is initially displaced 10
cm above the equilibrium point before the mass is attached, and
given a downward velocity of 1 m/sec. Find its displacement for
t>0.
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution
of
the second order linear differential equation:
(y'') + ( 6y') + (-27y) = ( 2) + ( -3)x. Find A,B,F,G,
where
A>B. This exercise may show "+ (-#)" which should be enterered
into
the calculator as "-#", and not "+-#". ans:4