Find Particular Solution of Y 4-81y
Question
Find the general solution of y(4) 81y = 0
Find the general solution of y(4) 81y = 0
Answers
Find the general solution of the given equation. $$y^{\prime \prime}=0$$
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Welcome to this lesson in this lesson. We have the first saw that the french I question that would want to find the general solution of. So here we compare it to a general form Y. Prime plus P of X. Y. Is equal to Q. Of X. So here the P. Of X. When comparing to this becomes negative B. To the bar X. Right. Then The Kovacs also becomes zero. Mhm. So we have the fact that that we would introduce which is equal to the integral P. Of X. Dx. So this is the call to integral negative if X. Dx and that's called negative E flex. So yeah why would be caught one over E. Each of X. Mhm. Yeah. Yeah. Then in to grow. Okay heated uh H of X. Care of X. Ds. So why is he called to one over eat the power negative E. five x. done integral. You this is negative E. To the X. Times zero E. X. So this is E then E. F. X. So the negative goes up. When it comes up it becomes positive. So the whole thing here becomes zero plus. See the observe plus some constant and why finally becomes C. Then E. To the bar E. X. Okay so some short time this is the end of the lesson
You are given The differential equation. Why prime prime plus two I prime minus eight Y. Is he going to 0? Now writing the characteristic equation? We have R squared plus To our -8 is equal to zero. And we have to find the roots for this characteristic equation. We know that to find the roots, we need Two numbers that give a product of -8. We'll see. And is some of positive two years, I will be here. No. We know that four and minus to give us a product of -8 and they do give us a sum of positive too, substituting them for two hours. Here we have arab squared plus four. AR -2 -8 is going to zero. And here if we fact arise We will have another plus four and para minus two Which will be equal to zero and our roots will be -4 and positive too. Now using these routes, we know that since they are real and distinct, the general solution will be in the form. Whitey is equal to C1, E. To the power parity plus C two. We are this is another one, C two, E. To the power of Arab to T. And here are roots uh minus four and positive too. And this is our general solution to these differential equation
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Consider T : RS 3 R , T (T,y,2) = (y + 22,y + 2z + 32, 2 + 3c,= I + 2y + 32) . Suppose {Wj_ is the standard basis for R4 Find a basis V1, U2, U3 for R3 such that M (T) with respect to the basis {v;} and {Wj}...
Find Particular Solution of Y 4-81y
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