Question

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

Answer #1

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

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

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

Find a general solution to the given equation for t<0
y"(t)-1/ty'(t)+5/t^2y(t)=0

solve the given initial value problem. y(cos2t)e^ty -
2(sin2t)e^ty + 2t + (t(cos2t)e^ty - 3) dy/dt = 0, y(0)=0

Use variation of parameters to find a general solution to the
differential equation given that the functions y 1 and y 2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
ty"-(t+1)y'+y=30t^2 ; y1=e^t , y2=t+1
The general solution is y(t)= ?

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

Use variation of parameters to find a general solution to the
differential equation given that the functions y1 and y2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
y1=et y2=t+1
ty''-(t+1)y'+y=2t2

Consider the differential equation y′′+ 9y′= 0.(
a) Let u=y′=dy/dt. Rewrite the differential equation as a
first-order differential equation in terms of the variables u.
Solve the first-order differential equation for u (using either
separation of variables or an integrating factor) and integrate u
to find y.
(b) Write out the auxiliary equation for the differential
equation and use the methods of Section 4.2/4.3 to find the general
solution.
(c) Find the solution to the initial value problem y′′+ 9y′=...

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