Recent content by berlinvic

Here is everything I've got so far: I reduced the system to the second order ODE $$ y_1''+y_1=\frac{1}{\cos x}. \tag{1} $$ Next steps: 1. Find two linearly independent solutions to the homogeneous equation ##y_1''+y_1=0## --- for instance, ##u(x)=\cos x## and ##v(x)=\sin x##; 2. Compute the...

Yes, I should have mentioned, I already know I should use variation of parameters. However I am not entirely sure which ones and how to apply them. I am fairly confused about it, do you have any tips?

Yes, but I still can't see how to move forward, I am just stuck at this line.

But I don't see how I can solve ##y_1^{\prime\prime}=y_2^{\prime}=-y_1+\frac1{\cos(x)}## using elimination method. Any help? I get the same answer as using https://mathdf.com/dif/, which, according to my professor, is incorrect.

I am trying to solve this system of differential equations using elimination method, but I am stuck. $$\begin{cases} y'_1 = y_2, \\ y'_2 = -y_1 + \frac{1}{\cos x} \end{cases}$$ Here's what I tried: I've been suggested to differentiate the ##y_1'= y_2## again to get ##y_1''= y_2'=...

I don't think so based on that, v_1 and v_2 here are some constants not volumes.

No, sorry for confusion. In the picture I attached those are ##x=\frac{1}{2}(v_1^2-v_2^2), v_1=const## and ##y=v_1v_2, v_2=const##

I think I posted everything that I've worked so far. The main equation for othogonality is the multiplication of derivatives of the curves equal to minus one, I mentioned it in the post as well. Additionally, I attached the photo where I show my work trying to parametrize the curves, but I'm...

I am asked to prove orthogonality of these curves, however my attempts are wrong and there's something I fundamentally misunderstand as I am unable to properly find the graphs (I have only found for a, but I doubt the validity). Furthermore, I am familiar that to check for othogonality (based...