Question #2. Solve the following differential equation de(1-2y Question 7 #3 Find a general solution to...
Find the general solution of the following differential equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? + ?e^(-t). (please solve Question No.7 only) 7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...
Find a general solution to the differential equation. 1/2y" +2y=2 tan 2t-1/3e2t The general solution is y(t) = _______
Question 7 Find the general solution of the given differential equation. y" +2y' +5y=0
3- Find the general solution of the given differential equation 3-2) y'' −2y' +y = e^t /(1+t^2)
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
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.
j Solve for the general solution to the differential equation below: y" - 5'- 2y + 2y = 0
(10 pts) Find the general solution to the differential equation ty'+2y =t^3 What are the homogeneous solutions?
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.
Question 2: Differential Equations a) (3 points) Find the general solution to the equation. Use C,C1,C2 ... to denote arbitrary constants as necessary. y"(t) = sin6t + 20e b) (5 points) Solve the following separable differential equation for the given initial condition. y')= (1) = 0 c) (5 points) Solve the following first-order linear differential equation for the given initial condition. y't) + 7y - 3,y(0) - 1 d) (2 points) State the equilibrium solution and whether it is stable...