Use method of undetermined coefficients to find a particular
solution of the differential equation ?′′ + 9? = cos3? + 2. Check
that the obtained particular solution satisfies the differential
equation.
Use the method of variation of parameters to find a particular
solution of the given differential equation and then find the
general solution of the ODE.
y'' + y = tan(t)
Use the one solution given below to find the general solution of
the differential equation below by reduction of order method:
(1 - 2x) y'' + 2y' + (2x - 3) y = 0
One solution: y1 = ex
Find the particular solution of the first-order linear
differential equation for
x > 0
that satisfies the initial condition. (Remember to use
absolute values where appropriate.)
Differential Equation Initial Condition
x dy = (x + y + 7) dx
y(1) = 6
y =
For each of the following differential equations, find the
particular solution that satisfies the additional given property
(called an initial condition).
y'y = x + 1
Using variation of parameters, find a particular solution of the
given differential equations:
a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) =
2e-2t (2e5/2 t - 5t - 2)
b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) +
3sin(t))et )
Please show work!