Consider the differential equation: d y 6y--6 exp-2). d t 6.1 (1 mark) Find a solution of the form y(t) - Cp exp(-2t) f...
Find a general solution to the differential equation. y'' – 6y' +9y=t-5e3t The general solution is y(t) =
Find a general solution to the differential equation. y'' - 6y' +9y=t-7e3t The general solution is y(t)=.
The solution of a certain differential equation is of the form y(t)=a exp(3t) + bexp(8t), where a and b are constants.The solution has initial coniditons y(0) and y’(0)=1.Find the solution by using the initial conditions to get linear equations fro a and by(t)=?
2 (6 points) Determine a suitable form for a particular solution of the differential equation y" + y 3 sint-1e-2 +t sin(2t) e. Do NOT determine a particular solution, just write the form that you will use when looking for one.
Find the solution of the ordinary differential equation + ky = -2t cos 2t, d+2 dt subject to the initial conditions y(0) = y'(0) = 0, where k is a constant, with k > 4, k + 8.
1. (9) Find the general solution to the differential equation. 1) y" - 6y' +9y = 0 2) y" - y' - 2y = 0 3) y" - 4y' + 7y = 0
Determine the form of a particular solution for the differential equation. Do not solve. y" - 18y' + 82y = et + tsin 2t - cos 2t The form of a particular solution is yp(t)= (Do not use d D. e. Ei or las arbitrary constants since these letters already have defined meanings.)
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6 when 0 (1 point) The differential equation can be written in differential form: M(x, y) dz +N(z, ) dy-0 where ,and N(x, y)--y5-3x The term M(, y) dz + N(x, y) dy becomes an exact differential if the left hand side above is divided by y4. Integrating that new equation, the solution of the differential equation is E C
Find
the general solution of the following non-homogeneous differential
equation d 2 y dt2 + 2 dy dt + y = sin (2t). (2) Now, let y(t) be
the general solution you find, when happen if we take lim t→+∞
y(t)?
2. Find the general solution of the following non-homogeneous differential equation dy dy sin (2t) (2) 2 +y= dt dt2 Now, let y(t) be the general solution you find, when happen if we take lim y(t)? t-++oo
Find a general solution to the differential equation. 1/2y" +2y=2 tan 2t-1/3e2t The general solution is y(t) = _______