Exercises

01

Method of power series: series terminates

Look for a power series solution to $x{y}^{\prime }=y$. Then solve the equation algebraically using prior methods we have learned, and compare your answers.

02

Method of power series: encountering problems

Look for a power series solution to $x^2{y}^{\prime }=y$. Then solve the equation algebraically using prior methods we have learned, and compare your answers.

03

Method of power series: one free coefficient

Find a power series solution to $y^{\prime }-\frac{1}{x}y=x^2$. Then solve the equation algebraically using prior methods we have learned, and compare your answers.

04

Method of power series: missing negative power

Find a power series solution to $y^{\prime }+\frac{1}{x}y=x$. Then solve the equation algebraically using prior methods we have learned, and compare your answers.