- #1

rygza

- 38

- 0

## Homework Statement

A linear equation in form:

dy/dx + P(x)y = 0 is said to be homogeneous since Q(x)=0.

a) show that y=0 is a trivial solution (wasn't even taught what a trivial solution is)

b) show that y=y

_{1}(x) is a solution and k is a constant, then y=ky

_{1}x is also a solution.

c) show that if y=y

_{1}x and y=y

_{2}x are solutions, then y=y

_{1}x + y

_{2}x is a solution

I don't even know how to start this problem. For part a) i simply plugged in 0 for y and got dy/dx=0 . doesn't seem right. then i tried separation of variable and got stuck at

(1/y)dy=-P(x)dx

can someone please guide me through? i have about three other problems like this and i haven't got a clue how to solve them.

p.s. that's y(sub1) and y(sub2)