
PLEASE RATE and VOTE
HW ty --te I.C. y(o) = 0 fly,t). & find analytical solution for this ode in...
Given that yı(t) =ť is a solution to the ODE: ty' + 4ty – 10y = 0, use the reduction of order method to find another solution y2 corresponding to the initival values ya(1)=- and y(1)= y2(t) =
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
Q4 a) Find the general solution of the differential equation Y') + {y(t) = 8(6+1)5; 8>0. Y'8 8 >0. 8(8-1)3 b) Find the inverse Laplace transform y(t) = £ '{Y(3)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te, y(0) = 0, y(0) = 1, for t > 0. You may use the above results if you find them helpful....
h Bessel equation of order p is ty" + ty + (t? - p2 y = 0. In this problem assume that p= 2. a) Show that y1 = sint/Vt and y2 = cost/vt are linearly independent solutions for 0 <t<o. b) Use the result from part (a), and the preamble in Exercise 3, to find the general solution of ty" + ty' + (t2 - 1/4)y = 3/2 cost. (o if 0 <t < 12, y(t) = { 2...
Q1: Find the general solution to the ODE: y'' + 4y' + 13y = 0.
any help on these two questions please??
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b) Find the general real solution of the linear ODE x(t)-Ax(t) + b(t). (c) Solve the initial value problem x(t) = A2(t) + b(t), x(0) = (-2,0,2)T 4.5: Determine the general solution of the ODE x"(t)-x"(t)-r(t) + x(t) = t cost.
4.4: Let 1 0 1 and b(t)- -1 1 0...
Find y(t) solution of the initial value problem 2 y2 +bt2 y'= y(1) = 1, t>0, ty
please help me with the ODE including PHYSICS
Thank you so much.
Thank you.
k r (0) o, r(0) 10. Find the solution of the following ODE: mř Vo + = 2(t) mr3(t) nr-
k r (0) o, r(0) 10. Find the solution of the following ODE: mř Vo + = 2(t) mr3(t) nr-
7. (10 points) Find a particular solution yp(t) to the nonhomogeneous equation ty + y - y = 24t*, t> 0, given the fact that the general solution of the associated homogeneous equation is yn(t) = cit + cat-, C1, C2 E R