Section 1.2 & 1.3

Problem 1:

a. $ \frac{d^2 y}{d x^2} + 2 \frac{d y}{d x} \frac{d^3 y}{d x^3} + x = 0 $

Isolating highest order,

$ y”’ = \frac{y”}{2y} – \frac{x}{2y} $

3rd order

b.$ y” – 3y’ + 2y = x^7 $

Isolating highest order,

$ y”= 3y’ -2y+x^7 $

2nd order

c. $ y’ – y^7 = 0 $

Isolating highest order

$y’ = y^7 $

1st order

d. $ y”y – (y’)^2 =2 $

Isolating highest order,

$ y” = \frac{2}{y} + \frac{(y’)^2}{y} $

2nd order