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Much appreciate your efforts!

Thank you Sir!

Thank you so much ✨

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@MathTutor1

2 жыл бұрын

Glad that it helps. Good luck with your studies. Thank you.

Thank you so much sir!!

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Very nice ......just cleared all my doubts in one video .... thankyou 🥳

@MathTutor1

Жыл бұрын

Thank you.

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@MathTutor1

2 жыл бұрын

Thank you.

How do you find the value of y1

@MathTutor1

2 жыл бұрын

That's a good question. We find this one using a trial-and-error argument and normally call the 'easy' solution. We find the difficult one using the formula. I hope this helps.

The proof can be found at kzread.info/dash/bejne/h2qIt8mpiNbIn7Q.html

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y = e ^ x is a solution of (d ^ 2 * y)/(d * x ^ 2) - 2 * d/dx (y) + y = 0 Find its other independent solution Can i use your formula for the following question?

@MathTutor1

8 ай бұрын

This is a very interesting problem. Did you see what happens? Since its a repeated λ problem, something strange will happen. So, the answer to your problem is yes. You should get y = xeˣ as the other solution. We normally solve this type of problems using the characteristic equation. I hope this helps. Thank you.

@carultch

8 ай бұрын

Given: y" - 2*y' + y = 0 Let function v(x) be defined, such that the two solutions relate to each other as follows: y2(x) = v(x)*y1(x) where y1(x) = e^x Take derivatives of y2(x): y2(x) = v(x)*e^x y2'(x) = v(x)*e^x + v'(x)*e^x = (v(x) + v'(x))*e^x y2"(x) = (v(x) + v'(x))*e^x + (v'(x) + v"(x))*e^x = [v(x) + 2*v'(x) + v"(x)]*e^x Apply to original diffEQ: [v(x) + 2*v'(x) + v"(x)]*e^x - 2*[(v(x) + v'(x))]*e^x + v(x)*e^x = 0 Everyone brought e^x to the party: [v(x) + 2*v'(x) + v"(x)] - 2*[(v(x) + v'(x))] + v(x) = 0 Cancel terms that add to zero: v"(x) = 0 Integrate twice and get: v(x) = C1*x + C2 Thus if y1(x) = e^x, then in the case of C1 = 1 and C2 =0, then y2 = x*e^x. Since we form a linear combination of y1 and y2, to get y, the two arbitrary constants ultimately get absorbed in the arbitrary coefficients on y1 and y2 as we add them together.

Why p(X)=0

@MathTutor1

3 жыл бұрын

I guess you are referring to example 1. You may notice that there is no y' term there. So the coefficient function p(x) =0. I hope it is clear now. Thank you.

@UzmaAliraza265

3 жыл бұрын

@@MathTutor1 thanku Sir.I was watching for other method not the formula..can you provide 1st method