**Unformatted text preview: **MEC702 Wk 6 Tutorial Homogeneous Linear ODE with Constant Coecients. 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 Coecients. Find a general solution y = yh + yp where yp is found using the Method of Undetermined Coecients.
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.
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- Winter '16
- Alveen Chand
- general solution, Nonhomogeneous Linear ODEs, Wronskian. Linear Independence