for y(t) function ty'' - ty' + ty = 0, y(0)= 0 , y'(0)= 1
solve this initial value problem by using Laplace Transform.
(The equation could have been given such as "y'' - y' + y = 0" but
it is not. Please, be careful and solve this question step by
step.) )
Let y′=y(4−ty) and y(0)=0.85.
Use Euler's method to find approximate values of the solution of
the given initial value problem at t=0.5,1,1.5,2,2.5, and 3 with
h=0.05.
Carry out all calculations exactly and round the final answers
to six decimal places.
3. Consider the IVP:
dy =ty^1/3; y(0)=0,t≥0. dt
Both y(t) = 0, (the equilibrium solution) and y(t) =
?(1/3t^2?)^3/2 are solutions to this IVP.
(a) Show that the trivial solution satisfies the IVP by first
verifying that it satisfies the initial condition and then
verifying that it satisfies the differential equation.
(b) Show that the other solution satisfies the IVP again by
first verifying it satisfies the initial condition and then
verifying that it satisfies the differential equation.
(c) Explain...
initial value problem
y'=ty(4-y)/3, y(0)=y_0
determine the behavior of solution as t increases depends on the
initial value y_0
The answer says that y->-infinite when y_0<0. but i cannot
understand. please explain it