y (d^2 y/dx)−9y = 3


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Question Number 92468 by jagoll last updated on 07/May/20

$y \frac{d^{2} y}{dx} - 9 y = 3$
	Answered by mr W last updated on 07/May/20

	$u = \frac{d y}{d x}$ $y u \frac{d u}{d y} - 9 y = 3$ $u \frac{d u}{d y} = \frac{3}{y} + 9$ $u d u = 3 (\frac{1}{y} + 3) d y$ $\int u d u = 3 \int (\frac{1}{y} + 3) d y$ $\frac{u^{2}}{2} = 3 (\ln y + 3 y + C_{1})$ $u = \frac{d y}{d x} = \pm \sqrt{6} \sqrt{\ln y + y + C_{1}}$ $\int \frac{d y}{\sqrt{\ln y + 3 y + C_{1}}} = \pm \sqrt{6} \int d x$ $\int \frac{d y}{\sqrt{\ln y + 3 y + C_{1}}} = \pm \sqrt{6} x + C_{2}$ $. . . .$
	Commented by jagoll last updated on 07/May/20

	$tobe continue sir$
	Commented by mr W last updated on 07/May/20

	$n o a n t i d e r i v a t i v e w i t h e l e m e n t a r y$ $f u n c t i o n s!$
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