Higher Order Linear Differential Equations

  1. Find the general solution of the differential equations. Let \(D = \dfrac{d}{dt}\). View Solution
    • \( y'''+y''-4y'-4y=0 \)
    • \( y^{(4)}-5y''+4y=0 \)
    • \( (D^2+D-6)(D^2+5)y=0 \)
  2. Find the solution of the given initial value problem (IVP).
    • \( y'''+4y'=0, \quad y(0)=0, y'(0)=1, y''(0)=2 \) View Solution
    • \( y^{(4)}- y=0, \quad y(0)=0, y'(0)=0, y''(0)=1, y'''(0)=1 \) View Solution
  3. Show that the general solution of \(y^{(4)}-y=0\) can be written as: \(\displaystyle{ y=A\cos t + B\sin t+C\cosh t + D\sinh t}\) View Solution
  4. Given the list of roots and their multiplicities of the characteristic equation, find a general solution. What is the order of the corresponding ODE? (\( k_i = \) multiplicity of root \(r_i\))
    \[ r_1=-2, k_1=3; \quad r_2=1, k_2=2; \quad r_{3,4}=-1\pm 5i, k_{3,4}=1 \]
    View Solution