3.1 Problems
In Problems 1 through 10, find a power series solution of the given differential equation. Determine the radius of conver- gence of the resulting series, and use the series in Eqs. (5) through (12) to identify the series solution in terms of famil- iar elementary functions. (Of course, no one can prevent you from checking your work by also solving the equations by the methods of earlier chapters!)
1 y = y
3. 2y+3y=0
5. y' = x2y
7. (2x-1)y'+2y=0 9. (x-1)y+2y= 0
2. y=4y
4. y+2xy=0 6. (x2)y'+y=0
8. 2(x+1)y'y 10. 2(x-1)y' = 3y
In Problems 11 through 14, use the method of Example 4 to find two linearly independent power series solutions of the given differential equation. Determine the radius of convergence of each series, and identify the general solution in terms of famil-