Home assignment 3. Deadline is 03/30 1. Solve Euler Equation t 2 y'' t y' + y = 0, 2. Solve Euler Equation 2 t 2 y'' + 3 t y' y = 0, t 0 t 0 3. Use the method of reduction of order to find the general solution of the equation y'' y' + y x =0 if one of its solutions is known: y1 x . 4. Find the general solution of the given differential equation. y'' 6y' 7y = 15e2t 5. Find the general solution of the given differential equation. y'' + 2y' + 5y = 3 sin 2t 6. Find the general solution of the given differential equation. y'' y' 2y = 2t + 4t2 7. Find the general solution of the given differential equation. y'' 2y' 3y = 3tet 8. Problems # 7 (P. 203, Section 3.7) 9. Problem #28 (a, b, and question (c) is optional) ( P. 206, Section 3.7) 10. Problem # 18 (a, b) (P. 218, Section 3.8) 11. Verify that the given functions are solutions of the differential equation, and determine their Wronskian. x3y''' + x2y'' 2xy' + 2y = 0; y1 = x, y 2 = x2, y3 12. Find the general solution of the given differential equation. y''' 3y'' 9y' + 27y = 0 13. Solve the initial value problem: y''' 3y'' + 3y' y = 0, y 0 1, y 0 3, y 0 11 14. Find the general solution of the given differential equation. y(4) 8y''' + 16y'' = 0 15. Find the general solution of the given differential equation. y(4) + 8y'' + 16y = 0 16. Find the general solution of the given differential equation. y(6) + y'' = 0 7 x