[chippy22]

Basicaly I am struggling with some Second Order Differential Equations, and was wondering whether a kind soul would be able to help me out.

I need to find the general equation of the following using the substitution given, where v is a function of x:

1. x dy/dx=x+y, x>0; y=vx


2. x^2 (d^2 y)/(dx^2 ) + x dy/dx + 6y = 0; x=e^v


3. Given that y=1 at x=2, use the substitution v=3x-y-3 to solve the differential equation:
(3x-y-1) dy/dx=(3x-y+3)


Thanks Chippy

[insparato]

(Original post by chippy22)
Basicaly I am struggling with some Second Order Differential Equations, and was wondering whether a kind soul would be able to help me out.

I need to find the general equation of the following using the substitution given, where v is a function of x:

1. x dy/dx=x+y, x>0; y=vx


2. x^2 (d^2 y)/(dx^2 ) + x dy/dx + 6y = 0; x=e^v


3. Given that y=1 at x=2, use the substitution v=3x-y-3 to solve the differential equation:
(3x-y-1) dy/dx=(3x-y+3)


Thanks Chippy

What have you done ? Do you understand what you're supposing to be doing and why the method works ?

You are trying to get rid of a variable by a substitution, to make the differential equation easier to handle.

Have a go at all three and post your workings if you get stuck.