Second Order Linear Differential Equations

Reduction of Order

View Formula Derivation (Video)
  1. Use the method of reduction of order to find a second solution of the given ODE.
    • \(t^2 y''- 4 t y' + 6 y=0, \quad t\gt 0; \quad y_1(t)=t^2\) View Solution
    • \( t^2y''+2ty'-2y=0, \quad t \gt 0; \quad y_1(t)=t\) View Solution
    • \(t^2 y''- t(t+2)y'+(t+2)y=0, \quad t\gt 0; \quad y_1(t)=t \) View Solution
  2. Verify that \(y_1(t)=\sin (t^2)\) is a solution of the ODE \( ty''-y'+4t^3y=0, \quad t \gt 0\). Use the method of reduction of order to find a second linearly independent solution.
    View Solution