Second order linear diff equations: Reduction of Order:
1. Use the method of reduction of order to find a second solution of
the given ODE.
a. \(t^2 y''- 4 t y' + 6 y=0, \: t>0; \quad y_1(t)=t^2\)
solution
b. \( t^2y''+2ty'-2y=0, \: t>0; \quad y_1(t)=t\) solution
c. \(t^2 y''- t(t+2)y'+(t+2)y=0, \: t>0; \quad y_1(t)=t \)
solution
2. Verify that \(y_1(t)=\sin (t^2)\) is a solution of the ode
\( ty''-y'+4t^3y=0, \quad t>0\). Use the method of reduction of order to
find a second linearly independent solution of the ode.
solution