good afternoon colleagues engineers I would like you to help me with some problems of the class of Differential Equations.

-First Order Differential Equation Topic

In these exercises by substitution, each

one of the given functions is a solution of the given differential equation. In these problems, premiums mean the

derivative with respect to x

1. y ^ '\: ^' = 9y \:; \: y \: _ 1 = \: e ^ {3x}, \: y \: _ 2 = e ^ {- 3x}

2. x ^ 2y '' \: + \: 5xy '\: + \: 4y \: = \: 0; \: y_1 \: \: = \: \ frac {1} {x ^ 2} \ :, \: y_2 = \: \ frac {lnx} {x ^ 2} \:

-Integral theme as general and particular solutions

find the function and! f (x) that satisfies the given differential equation and the prescribed initial condition.

1. \ frac {dy} {dx} \: = \: \ frac {1} {x ^ 2}; \: y \ left (1 \ right) \: = \: 5

2. \ frac {dy} {dx} \: = \: cos \: 2x; \: y \ left (0 \ right) \: = \: 1

help