# 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 other substitutions.
2. Solve first-order differential equations using an integrating factor.
3. Solve first-order nonhomogeneous differential equations using the two-step method.
4. Solve Bernoulli equations.
5. Find orthogonal trajectories.
6. Solve second-order and higher order homogeneous differential equations using an auxiliary equation.
7. Solve linear and nonlinear applications..
8. Solve the Cauchy-Euler differential equation.
9. Solve second-order and higher order nonhomogeneous differential equations using the methods of reduction of order, variation of parameters, operators and annihilators, and undetermined coefficients.
10. Solve systems of constant coefficient differential equations using matrix methods.
11. Use Laplace transforms to solve differential equations and systems of differential equations with initial conditions.
12. Use power series methods, including the method of Frobenius, to solve differential equations.
13. Use Euler’s method, Improved Euler Method, and Runge-Kutta methods to solve differential equations 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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