Question

Find the general solution of the equation.

d^2y/dt^2-2t/(1+t^2)*dy/dt+{2/(1+t^2)}*y=1+t^2

Answer #1

find the general solution of the differential equation dy/dt -
2y = t^2 * e^2t

dy/dt - 2y = 7e^(2t)
a. Determine the general solution to the associated homogeneous
equation.
b. By choosing an appropriate guess, determine a particular
solution to this differential equation.
c. Using your answers from parts (a) and (b), write down the
general solution to the original equation
d. Check that your solution is correct by plugging it into the
original ODE.
e. Determine the specific solution corresponding to the initial
condition y(0)= 3
Pls explain how you did it

Consider the differential equation. Find the solution y(0) =
2.
dy/dt = 4t/2yt^2 + 2t^2 + y + 1

Find the general solution to the following:
[(e^t)y-t(e^t)]dt+[1+(e^t)]dy=0

Find the general solution to the system:
dx/dt = -4x + 3y
dy/dt = -5x/2 + 2y

Find the general solution to the given differential
equation. 1+(1+ty)e^ty+(1+t^2e^ty) dy/dt=0

Find the general solution: y'' - (2t/(1+t^2)) y' +
(2/(1+t^2)) y = 1+t^2

Consider the linear system
dY/dt=(0 2 −2 −1)Y
(a) Find the general solution.
(b) Find the particular solution with the initial value
Y0=(−1,1).

2 d2y/dt2 + 2 dy/dt + 2y = sin(2t)
in steps please

Use the method of reduction of order to find the
general solution of the following differential equation. (t^2)
d^2y/dt^2 + t dy/dt + (t^2-1/4) y = 0, y1(t) = sin t/sqrt(t)

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