Find two power series solutions of the given differential equation about the ordinary point x = 0. y" - 3xy' + y = 0 +... and y, = x+** 15 2x5 2x? + 91x5 + *... 2 24 720 3 45 x* 5x3 and y; = x ++. 2x°, 2x13 11x12 O y, = 1. + 24 144 15 45 x² . 7x* 91x5 x* . 8x7 O y, = 1+ 2 +... and y, = x + + + + + 24 720 3 63 x2 Y, =1- 5x* 11x5 and Y2 = x3 2x. 2x7 + 24 144 15 45 x2 O y, = 1 2x. x, 8x7 11x5 and Y2= = x + 3 + 24 144 63

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.