Solve the given boundary-value problem. y double prime + 3y = 9x, y(0) = 0, y(1) + y prime (1) = 0.
Determine the inverse Laplace transform of F(s) = \frac{3s+5}{s^2+4s+13}
Find y_c and y_p by solving the differential equation x^2y'' + 10xy' + 8y = 0 using Cauchy Euler's rule.
Solve the differential equation 2y'' -5y' -3y =0 with the initial conditions y(0) = 1, y'(0) =10
Solve the given differential equation. (6x) dx + dy = 0. (Use C as the arbitrary constant.)
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