Transcription of USING SERIES TO SOLVE DIFFERENTIAL EQUATIONS
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USING SERIES TO SOLVE DIFFERENTIAL EQUATIONS
USING SERIES TO SOLVE DIFFERENTIAL EQUATIONSMany DIFFERENTIAL EQUATIONS can t be solved explicitly in terms of finite combinations ofsimple familiar functions. This is true even for a simple-looking equation likeBut it is important to be able to SOLVE EQUATIONS such as Equation 1 because they arise fromphysical problems and, in particular, in connection with the Schr dinger equation in quan-tum mechanics. In such a case we use the method of power SERIES ; that is, we look for asolution of the formThe method is to substitute this expression into the DIFFERENTIAL equation and determine thevalues of the coefficients Before USING power SERIES to SOLVE Equation 1, we illustrate the method on the simplerequation in Example 1 Use power SERIES to SOLVE the equation.
USING SERIES TO SOLVE DIFFERENTIAL EQUATIONS Many differential equations can’t be solved explicitly in terms of finite combinations of simple familiar functions.
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