Suppose $_1,p_2,q_1$ and $q_2$ are continuous on $(a,b)$and the The equations $y''+p_1(x)y'+q_1(x)y=0$ and $y''+p_2(x)y'+q_2(x)y=0$ have the same solution on $(a,b)$ then $p_1=p_2$ and $q_1=q_2$
What i am tried
I am using trying prove this by Able's formula
for first equation $W[y_1,y_2](x)=c_1 e^{-\int p_1(x)dx}$
and for second equation $W[y_1,y_2](x)=c_2 e^{-\int p_2(x)dx}$
Since he equations $y''+p_1(x)y'+q_1(x)y=0$ and $y''+p_2(x)y'+q_2(x)y=0$ have the same solution on $(a,b)$
is it $W[y_1,y_2](x)=W[y_1,y_2](x) \Rightarrow p_1(x)=p_2(x)$ is i am coorect