#### Quasar Chunawala

##### Well-Known Member

Hi folks,

I tried to come up with a proof for the following statement. But, I am facing trouble proceeding with the arguments. It would be nice, if someone could help. Pardon me for posting the question here, as there's no math sub-forum here.

Q. Show that two

**distinct solutions**of a normal first order linear differential equation cannot have a point of intersection.

*Proof.*

Let \(L=a_{1}(x)D+a_{0}(x)\) be the linear differential operator of the first order and let

\[ Ly=h \]

be the given differential equation.

Suppose \(f(x)\) and \(g(x)\) are two distinct solutions of the linear differential equation, such that

\[Lf=h, \text{whenever }y(x_1)=k_1\]

\[Lg=h, \text{whenever }y(x_2)=k_2\]

But, I don't know where to go from here. Any tips on how to proceed would help me.

Thanks guys!