Solution steps plz 2. Solve the IVP (x" + x = 3uſt-27) |x(O)=0, x'(O)= 2
Solution steps plz k=0 x"+x=Ž8(t-2k1) 1. Solve the IVP x(0)=0, x'(0) = 0 and discuss the behavior of the oscillator's amplitude when t → 00.
Solution steps plz 5. Use Duhamel's formula to express the solution of the {x"-7x'+12x = f(t) generic IVP in integral form. 1*(0) = x'(O)=0
solve the IVP Q2) Solve the IVP. Show the steps of derivation, beginning with the general solution Xy' + y = 0, y(4) = 6 dr/dt = - 211. 7(0) = lo v' = -4x/y: V(2) = 3
a.) Solve the following IVP. X !=3x,-13x2 X, (O)=3 X2 = 5x +X2 X₂(0)=-10 b.) solve the following IVP. X;= -X, +(3/2) X2 X, (2)=1 X 2 = (-%6) xx-2x2 X2 (2)=0
please help and show steps 3. Solve the following IVP: ly'(0) = y'o, y(0) = yo where p > 0 and k 1. 2. Let k=0 Use the above power series to solve the following IVP. List the first six nonzero terms the solution the differential equation. ay = (t + y)2 ,y(0) = 0.
Solve the IVP y' + y = f(t), y(0) = 0, where f is the 27-periodic function given by f(t) -1, 0<t<T, <t<21, f(t) = f(t + 27).
2. Solve the IvP x()21 x(0) = | 1 t) = la x(t),
Consider the solution to the IVP y' - xy = x; y(0) = 2 Find y' (0) Consider the solution to the IVP y' - xy = t; y(0) = 2 Find y" (0)
Solve the IVP [:] =: -:] [:] [0]=[2]
please show steps Solve the IVP: y'-2fe'"y(t)dt =t, y(0) = 2 0