# MAT 250 Differential Equations

Exit Skills

1. Solve first-order differential equations, which are separable or can be made separable, using a linear substitution or rational substitution or others.
2. Solve first-order DE using an integrating factor.
3. Solve first-order nonhomogeneous DEs using the two-step method.
4. Solve Bernoulli equations.
5. Find orthogonal trajectories.
6. Solve second-order and higher-order homogeneous DEs using an auxiliary equation. Also, solve applications related to motion, springs and electrical circuits. Solve the Cauchy-Euler, DE.
7. Solve second-order and higher-order nonhomogeneous DEs using the methods of reduction of order, variation of parameters, operators and annihilators and undetermined coefficients.
8. Solve systems of constant coefficient DEs using matrix methods.
9. Use Laplace transforms to solve DEs and systems of DEs with initial conditions.
10. Use power series methods, including Methods of Frobenius, to solve DEs.
11. Use Euler’s method, Improved Euler Method and Runge-Kutta methods to solve DEs numerically.

Objectives

1. Solve first-order differential equations including those equations classified as separable, exact, linear, Bernoulli, homogeneous and Cauchy-Euler, using integrating factors where appropriate.
2. Solve higher-order constant coefficient homogeneous and nonhomogeneous differential equations using reduction of order, undetermined coefficients and variation of parameters.
3. Solve differential equations using power series including the method of Frobenius.
4. Solve systems of differential equations, including the method of Laplace transforms and the eigenvalue/eigenvector method.
5. Solve differential equations numerically, including Euler’s methods and Runge-Kutta methods.

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