Differential equations Homework 3
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Differential equations
Homework 3
1. Consider the following non-homogeneous differential equation:
with initial conditions
(a) [20 points] Find the general solution of the problem by using the method of undetermined coefficients.
(b) [20 points] Find the general solution of the problem by using the method of variation of parameters.
(c) [20 points] Find the general solution of the problem by using the Laplace transform.
2. Consider the beam bending equation
where F is the external force, EJ is the beam bending stiffness. Solve the equation for each of the following boundary conditions:
(a) [10 points] (Simply supported edges) w(0) = w′′ (0) = w(l) = w′′ (l) = 0;
(b) [10 points] (Cantilevered edges) w(0) = w′ (0) = w(l) = w′ (l) = 0;
(c) [10 points] (Simply supported-cantilevered edges) w(0) = w′′ (0) = w(l) = w′ (0);
(d) [10 points] (Cantilevered-free edges) w(0) = w′ (0) = w′′ (l) = w′′′ (l) = 0.
2023-07-21