m3354_f05_q2_sol

m3354_f05_q2_sol - u = u + t t Write the problem as u = u t...

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Math 3354 Sec. 2, Quiz # 2 Name 1. ( Separable Equation ) Solve the initial value problem u 0 = 2 u ( t + 1) , u (0) = 1. Separate variables to get du u = 2 dt t + 1 . Now integrate both sides to get ln( u ) = 2 ln( t + 1) + C = ln( t + 1) 2 + C. Now use u (0) = 1 so get 0 = 0 + C so C = 0. Exponential both sides and set C = 0 to get u = ( t + 1) 2 . 2. ( Homogeneous Equation ) Use y = u t to find the general solution of
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Unformatted text preview: u = u + t t Write the problem as u = u t + 1. Set y = u/t which implies u = ty + y Thus we get ty + y = y + 1. This equation is separable so we separate and integrate Z dy = Z dt t So y = ln( t ) + C and nally u = t (ln( t ) + C ) ....
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