205sp11-fake-ex1b-solutions

205sp11-fake-ex1b-solutions - A5GACCEEXA#B Ò ×ØÖÙ Ø...

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Unformatted text preview: A5GACCEEXA#B Ò ×ØÖÙ Ø iÓÒ × : h e×eÔ ÖÓb ÐeÑ ×ÖeÔ Öe×eÒ ØØh eØÝÔ e×Ó fÕÙ e×Ø iÓÒ ×ÝÓÙÑ igh ØÒdÓÒ Øh eÖ×Ø4 : eÜaÑ iÒ Øh i××eÑ e×Øe Ö×a Øh5h eÝa ÖeØak eÒd iÖeØ ÐÝ fÖÓÑ Ó Ðd eÜaÑ ×h eb e×ØÛ aÝ ØÓÙ ×e Øh i×ÖeÚ ieÛ i×ØÓÔ Öe ØeÒd Øha ØeahÓ fØh e×eÔ ÖaØ ieeÜaÑ ×a ÖeØh eÖea ÐØh iÒgaÒd Øak eØh eeÜaÑ Û iØhÓÙ Øae××ØÓÒÓ Øe×Ó ÖØh eØeÜ ØÓ ÖaÒÝÓ Øh e Öh e ÐÔh eÒÙ × iÒgÝÓÙ ÖÒÓ Øe×aÒd ØeÜ Øg Öad e ÝÓÙ ÖØÖ ia ÐeÜaÑA Ò ×Û e Ö×Û iÐÐb eÑ ad eaÚa iÐab ÐeÙ e×daÝÓÒ Øh eÛ ebÔage dy dx = xy y (0) = 2 Ó ÐÙ Ø iÓÒ : h i× i×a ×eÔa Öab ÐeeÕÙa Ø iÓÒ ; dy/y = xdx, Ó Ö ln | y | = 1 2 x 2 + C Ó Ö y = Ae x 2 / 2 h e iÒ iØ ia ÐÓÒd iØ iÓÒ × iÑ Ô ÐÝ Øha Ø A = 2 Ó Ö y = 2 e x 2 / 2 x dy dx = ln x y 2 Ó ÐÙ Ø iÓÒ : A ga iÒ ×eÔa Öab Ðe y 2 dy = ln( x ) 1 x dx. Ò Øeg Öa ØebÓ Øh × id e× y 3 3 = (ln( x )) 2 2 + C, Û h ih i×aÒaeÔ Øab Ðe×Ó ÐÙ Ø iÓÒ ØhÓÙghaga iÒÝÓÙaÒ ×Ó ÐÚ eeÜÔ ÐiiØ ÐÝ fÓ Ö y y = parenleftbigg 3 parenleftbigg (ln( x )) 2 2 + C parenrightbiggparenrightbigg 1 / 3 . y ′ + 1 x y = √ x 2 − 3 y (2) = 2 Ó ÐÙ Ø iÓÒ : h i×i×a ÐiÒ ea ÖeÕÙa Ø iÓÒ iÒe p ( x ) = 1 /x P ( x ) = ln( x ) aÒd Øh e iÒ Øeg Öa Ø iÒg faØÓ Ö i× μ = x ÓÛ e ÐÓÓka Ø ( xy ) ′ = xy ′ + y = x parenleftbigg y ′ + 1 x y parenrightbigg , aÒd Øh e ÖeØh e Ðe fØhaÒd × id eÓ fØh ed ie ÖeÒ Ø ia ÐeÕÙa Ø iÓÒaÔÔ ea Ö×eÔ Ðae iØbÝ Øh e Ö igh ØhaÒd × id eaÒd ( xy ) ′ = x radicalbig x 2 − 3 . A5GACCEEXA#B Ò Øeg Öa ØebÓ Øh × id e×aÒdÛ iØh Øh e×Ùb ×Ø iØÙ Ø iÓÒ u = x 2 − 3 xy = integraldisplay x radicalbig x 2 − 3 dx = integraldisplay √ u parenleftbigg 1 2 du parenrightbigg = 1 3 u...
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205sp11-fake-ex1b-solutions - A5GACCEEXA#B Ò ×ØÖÙ Ø...

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