# Thread: 1st order ODE

1. ## 1st order ODE

Does anyone know how to solve dy/dx=(x-y)/(x+y), with initial condition y(1)=-2. I am looking for an explicit form solution.

I get stuck when I separate the equations and have to the integrate 0dx but that doesnt make any sense

Many thanks guys

2. Originally Posted by MathsLion
Does anyone know how to solve dy/dx=(x-y)/(x+y), with initial condition y(1)=-2. I am looking for an explicit form solution.

I get stuck when I separate the equations and have to the integrate 0dx but that doesnt make any sense

Many thanks guys
Substitute y = xv. You will have an exmaple in your class notes or textbook (homogenous differential equation).

3. hi

what do you mean by let y=xv

where does v come into this? I am still confused

4. Originally Posted by MathsLion
hi

what do you mean by let y=xv

where does v come into this? I am still confused
You make the substitution y = xv in the differential equation.

Please go to your class notes or textbook first and spend some time reviewing this type of equation (I have told you its name and told you the technique). Then, if you are still confused, ask for more help.