Question

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

Answer #1

Find the general solution. Explain and show all steps.
[(e^t)y - t(e^t)] dt + [1 + (e^t)] dy = 0

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 of the equation.
d^2y/dt^2-2t/(1+t^2)*dy/dt+{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).

Find the general solution of the system
dx/dt = 2x + 3y
dy/dt = 5y
Determine the initial conditions x(0) and y(0) such that the
solutions x(t) and y(t) generates a straight line solution. That is
y(t) = Ax(t) for some constant A.

Are both of the following IVPs guaranteed a unique solution?
Explain. (a) dy/dt =y^ 1/3sin(t), y(π/2)=0. (b) dy/dt =y^1/3
sin(t), y(π/2)=4.

find the solution for the DE
dy/dt +ty^3 +y/t = 0
answer explicitly if passible

a). Find dy/dx for the following integral.
y=Integral from 0 to cosine(x) dt/√1+ t^2 ,
0<x<pi
b). Find dy/dx for tthe following integral
y=Integral from 0 to sine^-1 (x) cosine t dt

Solve the initial value problem
t^(13) (dy/dt) +2t^(12) y =t^25 with t>0 and y(1)=0
(y'-e^-t+4)/y=-4, y(0)=-1

dy/dt=x , dx/dt=6x-8y, x=1 and y=-1 when t=0

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