Find the general solution to the differential equation below: Tip: it is by series (94x2)/-2y = 0 (94x2)/-2y = 0
3. Find the general solution to the differential equation y"2y 0 as a power series about 0 involving two free constants; the formula for the nth coefficient need not be in 'simplified' form.
7. Consider the first order differential equation 2y + 3y = 0. (a) Find the general solution to the first order differential equation using either separation of variables or an integrating factor. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem 2y + 3y = 0, y(0) = 4.
Question 7 Find the general solution of the given differential equation. y" +2y' +5y=0
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Solve for the general solution to the differential equation below: y" - 5'- 2y + 2y = 0
Find the general solution to the differential equation: ty'+2y
=t3, and what are the homogenous solutions.
Find the general solution to the differential equation: ty'+2y = 3
Find a general solution to the differential equation. 1/2y" +2y=2 tan 2t-1/3e2t The general solution is y(t) = _______
(5 points) Find the general solution to the differential equation y" – 2y + 17y=0. In your answer, use Cį and C2 to denote arbitrary constants and t the independent variable. Enter Cų as C1 and C2 as С2. y(t) = help (formulas) Find the unique solution that satisfies the initial conditions: y(0) = -1, y'(0) = 7. y(t) =
3. For the differential equation (2x2 - 1)/" + xy + 2y = 0, find the first three non-zero terms of each of two linearly independent power series solutions. 4. Find the general solution of the system of equations
4. Consider the differential equation +2y + 2y = cost (a) (5 points) Find the general solution to the corresponding homogeneous equa- tion. (b) (5 points) Find a particular solution, y(t), to the non-homogeneous equation. (c) (2 points) Determine the general solution to the non-homogeneous equation.
3. Find the general solution of the differential equation y” + 2y' + y = 0 (a) y=ce' +c,e* (b) y= ce" + xe * (c) y = cxe* +c,e* (d) y= ce* +C,xe" (e) y=ce?* +c,e-2 (f) y= c,e + ,xe” (g) y=cxe?* +cze 2 (h) y= c,e + ,xe 21