MATH 0290 Final: Math 0290 Final Exam (0290) 1 Solution -201
Document Summary
Mention a type of the given di erential equation. (a) y . = x2y, y(0) = 8, where y = dy dx. Solution: y(x) = 8ex3 (b) t dx dt. Integrating factor is i = t 4, x(t) = t4 ln t + ct4, c = 5, x(t) = (ln t + 5)t4 (c) y 4y = 2e4t, y(0) = 3, y (0) = 11. 6 e4t: find the general solution to the equation y + 4y + 4y = 12t2 10. Solution: y = c1e 2t + c2te 2t + 3t2 6t + 2: a 1-kg mass when attached to a spring, stretches the spring to a distance of 4. 9 m. (a) calculate the spring constant. Solution: k = 2 (b) the system is plased in a viscous medium that supplies a damping constant = 3 kg/s. The system is allowed to come to rest.
