In problem 32, we show that the equation y" + p(t)y' + q(t)y = 0 can be transformed into the equation d²x + dx² dt² +p(t

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In Problem 32 We Show That The Equation Y P T Y Q T Y 0 Can Be Transformed Into The Equation D X Dx Dt P T 1 (57.23 KiB) Viewed 65 times

In problem 32, we show that the equation y" + p(t)y' + q(t)y = 0 can be transformed into the equation d²x + dx² dt² +p(t)- dx dt 2 coefficients using x = u(t) q'(t) + 2p(t)q(t) is a constant. 2(q(t))³/2 dx dy dt/ dx Use this result to try to transform the equation y" + 5tºy' + e-t¹y = 0, -∞ <t<∞ into one with constant coefficients. If this is possible, find the general solution of the equation. q' + 2pq 2q³/2 +q(t)y = 0, with constant = = [(a(t)) ¹/2² q(t))¹/² dt, provided the expression The equation can be transformed into one with constant coefficients because: = The general solution is: y(t) = Choose one