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MEC702_Wk_6_Tutorial

# MEC702_Wk_6_Tutorial - MEC702 Wk 6 Tutorial Homogeneous...

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Unformatted text preview: MEC702 Wk 6 Tutorial Homogeneous Linear ODE with Constant Coecients. λ-method. Solve the ODE. Find a general solution. 1. y00 + y0 + 3.25y = 0. 2. y00 + 1.8y0 − 2.08y = 0. 3. 4y00 − 4y0 − 3y = 0. 4. y00 + 9y0 + 20y = 0. 5. 9y00 − 30y0 + 25y = 0. Solve the IVP. Find the particular solution. 1. y00 + 25y = 0, y(0) = 4.6, y0(0) = −1.2. 2. y00 + y0 − 6y = 0, y(0) = 10, y0(0) = 0. Euler-Cauchy Equations. Solve the ODE. 1. x2y00 − 4xy0 + 6y = 0, y(1) = 0.4, y0(1) = 0. 2. x2y00 + 3xy0 + 0.75y = 0, y(1) = 1, y0(1) = −1.5. Wronskian. Linear Independence. Find the Wronskian. 1. e4x , e−1.5x . 2. e−0.4x , e−2.6x . Nonhomogeneous Linear ODEs. Method of Undetermined Coecients. Find a general solution y = yh + yp where yp is found using the Method of Undetermined Coecients. 1. y00 + 5y0 + 4y = 10e−3x . 2. 10y00 + 50y0 + 57.6y = cos x. 3. y00 + 3y0 + 2y = 12x2. Nonhomogeneous Linear ODEs. Method of Variation of Parameters. Find a general solution y = yh + yp where yp is found using the Method of Variation of Parameters. 1. y00 + 9y = sec 3x. 2. y00 + 9y = csc 3x. 1 ...
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• Winter '16
• Alveen Chand
• general solution, Nonhomogeneous Linear ODEs, Wronskian. Linear Independence

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