# hw5 - Week 5 2.5 Wronskian 3.1 Intro Slope Fields verify...

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Week 5: 2.5 Wronskian 3.1 Intro, Slope Fields, verify solution 3.2 Separable DE 3.4 Linear Equations

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2 Problem: Verify that the function y = c 1 x is a solution of y ± = y 2 x Solution: Compute y ± and check. y ± = c 1 ( 1 2 ) x - 1 2 . y 2 x = c 1 x 2 x = c 1 ( 1 2 ) x ( x ) 2 = c 1 ( 1 2 ) 1 x = y ± .
Problem: Inﬂamable substance, temp T 0 = 50 (F), placed in hot oven, temp T m = 450 (F). After 20 min substance temp T = 150 . Find temp at 40 min. If substance ignites at 350, ﬁnd time of combustion. Solution: Newton’s Law of cooling: T = T ( t ) temp at time t, dT dt = - k ( T - T m ) , T m = 450 , t in min.

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4 dT dt = - k ( T - T m ) , T m = 450 , T (0) = 50 , T (20) = 150 , ﬁnd T (40) and t c so T ( t c ) = 350 . Method: separation. dT T - T m = - k dt, ( T ± = T m ). integral: ln | T - T m | = - k t + c, T m = 450 . Initial Data: ln (450 - T ) = - k t + c, T (0) = 50 , T (20) = 150 .
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hw5 - Week 5 2.5 Wronskian 3.1 Intro Slope Fields verify...

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