Find the solution of the given IVP y" + 3y' + 2y = Uz(t); y(0) = 0, y'(0) = 1 + e-(t+2) e-2(t+2) + e 2 a. y=et-e-t + uz(t) [+ b. y=et +e-+ + uz(t) [ – e-(6-2) + že=2(t-2)] c. y = e-t-e-2t + uz(t) (2) - e-(4-2) + že=2(t-2)] + d. None of these
Find the first five terms of the series solution to the IVP (y +(1-2) +2y=e", y(0) = -5, (y0 =1, by making use of the general power series representation in (2). Hint: Recall the Taylor/power series for et about the point 0.
Problem 2: [Also challenging] Find the solution of the following IVP: y' +2y = g(t), with y(0) = 3 where g(t) = - 0<t<1: g(t) = te-2 > 1.
completeness and clarity 2. Find a particular solution for the IVP y" - 2y + 2y = 8(t - 5), y(0) = 0, y0) = 1
Laplace transform of the unit step function Y" + 3y' + 2y = uz(t).
slove it fast please Solve given IVP. (t +2y)dt +ydy=0; y(0)=1 and Select the correct value of c. O a. None 1 O b. 2 Oco Od. 1 O e. -1
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y" - 4xy' + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE " + 2y' - 15y = 3x 8. A 2...
The general solution to equation y" - 2y - 3y=0 is a. y=1e3! + ce- b. y=ce" + ce-1 C. y = c + c2e- d. none of the above
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...
Question 10 Find the differential equation of the given family y =C + 2 a)xy 3y +6=0 b) 2y-e-0 c)y+2y1=0 y+2y-1-0 d) y+2xy 1-0 f) None of the above. Question 11