Unformatted text preview: it has a repeated root. c. Continue the method of Frobenius to ±nd a solution y = f ( x ). HINT: The in±nite series for f ( x ) truncates to a polynomial. d. Rule 4 on page 15 of the notes applies here and says that a second linearly independent solution can be obtained in the form: y = f ( x ) log( x ) + g ( x ) Having found f ( x ) in part c above, substitute this expression into EQ.(*) and obtain an ODE on g ( x ). Solve it by looking for g ( x ) in the form of a Frobenius series. HINT: The in±nite series for g ( x ) truncates to a polynomial. e. Combine the above results to write the general solution of EQ.(*). Check your answer by substitution....
View Full Document
- Spring '08
- ORDINARY DIFFERENTIAL EQUATIONS, Complex differential equation, Frobenius method, Regular singular point, a. b. c., irregular singular point