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Note that our solution only works for y > 1 If y < −1 we can substitute v = −x to see that ev −e v ev − e−v = −y > 1 An identical calculation then yields 1 v = (ln((−y) 1) − ln((−y) − 1)) 2 1 x = − 2 (ln(−y 1) − ln(−y − 1)) 5 y = ex e−x Again we begin by applying the hint u = ex We solve for u Solution The characteristic equation of Equation 1322 is r2 3r 2 λ = 0, with zeros r1 = − 3 √1 − 4λ 2 and r2 = − 3 − √1 − 4λ 2 If λ < 1 / 4 then r1 and r2 are real and distinct, so the general solution of the differential equation in Equation 1322 is y = c1er1t c2er2tWords with only unique letters Choose a letter below to display all words without duplicate letters starting with that particular letter

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