MATH 4B Lecture Notes - Lecture 7: Constant Coefficients, Wronskian, Superposition Principle
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MATH 4B Full Course Notes
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Superposition principle for second order linea homogenous odes. Distinct real roots, complex roots, or repeated real values. Suppose that are a pair of solutions of. The linear combination is a solution for any constants. Verify that is a solution by substitution: is a linear homogenous equation is a solution. If at some point , then it is nonzero throughout the interval where. If are two solutions of the linear homogenous ode such that , then the constants can be uniquely determined so that satisfies any initial condition is the general solution. The solutions are a basis for the solution space. But are these all the solutions? the solution is defined. The solution space is a two-dimensional vector space. Check wronskian to determine if this is a fundamental set of equations. The solutions are called the fundamental set of solutions. Second order homogeneous linear ode with constant coefficients: Characteristic equation has pair of distinct real roots.
