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Solution steps plz k=0 x"+x=Ž8(t-2k1) 1. Solve the IVP x(0)=0, x'(0) = 0 and discuss the...
Solution steps plz
2. Solve the IVP (x" + x = 3uſt-27) |x(O)=0, x'(O)= 2
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
Please show all steps to solution.
7. Use a suitable Fourier Transform to find the solution of the IVP 2t-r-1 ,2-1 t 〉 0, , u(x, t), uz (x, t) 0asx→00, t〉0, →
7. Use a suitable Fourier Transform to find the solution of the IVP 2t-r-1 ,2-1 t 〉 0, , u(x, t), uz (x, t) 0asx→00, t〉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.
2. Solve the IvP x()21 x(0) = | 1 t) = la x(t),
9. Use a suitable Fourier Transform to find the solution of the IVP utt (x, t) Uz(0, t) u(x, t) , uz (z, t) 4uzz (x, t) + q (x, t), 0, t> 0, 0as x → 00, x > 0, t > 0, = = t>0. → = 0, ut (2,0)-( = { t, 0 0-x-2, -1, 0, > 2, u(x, 0) q(a, t) Leave your answer in the form of an integral.
9. Use a suitable Fourier Transform...
Solve the initial value problem (IVP) Ut + 3ux + 3u 0, u(x,0) = x2, (x, t) ER [0, +00).
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
solve the IVP using the Laplace approach
* +0.2 x = cos(4 t), x(0) = 1
7. Solve the initial value problem --( y = -1 00 when the initial value is given as following: and discuss the behavior of the solution as t (you may sketch the solution curve.) (a) X(0) = (0,0.5).
7. Solve the initial value problem --( y = -1 00 when the initial value is given as following: and discuss the behavior of the solution as t (you may sketch the solution curve.) (a) X(0) = (0,0.5).