Linear Algebra Question: y2=y1(integral (e^-integral P(x)dx)/y1^2)dx where y1 is a solution of y"+P(x)y'+Q(x)y=0. Show that y2 is a solution and that y1 and y2 are linearly independent. Hint: Find y2' and y2", and plug into y"+P(x)y'+Q(x)y=0, and for linearly independence find W(f1,f2).

Question

Linear Algebra Question: y2=y1(integral (e^-integral P(x)dx)/y1^2)dx  where y1 is a solution of y"+P(x)y'+Q(x)y=0. Show that y2 is a solution and that y1 and y2 are linearly independent. Hint: Find y2' and y2", and plug into y"+P(x)y'+Q(x)y=0, and for linearly independence find W(f1,f2).

rational · Answer

use the given hint ?

anonymous · Answer

sorry if this looks complicated but i wasn't sure how to get the integral symbol. But basically, I'm not sure how to take the derivative of y2.

anonymous · Answer

$$y2 = y1\int\limits_{?}^{?}(e^\int\limits_{?}^{?}P(x)dx) / y1^2$$

anonymous · Answer

wow that came out wrong