Page 65 - Schaum's Outline of Differential Equations

48 LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS [CHAR 6

it follows from the product rule of differentiation that the left side of (_/) equals —[e x)dx y]. Thus, (_/) can be
rewritten as x

Integrating both sides of (2) with respect to x, we have

or,

Finally, setting Cj = —c and solving (3) for y, we obtain

Solved Problems

In Problems 6.20 through 6.49, solve the given differential equations.

2
2
6.24. / + 3x y = 0 6.25. y' -x y = 0
6.26. / - 3x*y = 0

6.31. / - ly = e x

6.32. y'-ly= Ux 6.33. y'-ly = sin 2x

2
6.34. / + x y = x 2
6.36. y' = cos x 6.37. / + y = y 2

6.38. xy' + y = xy 3

6.40. / + y = y 2 6.41. y' + y = y 2
2
6.42. / + y = y e*