Second Order Homogeneous DEA linear second order homogeneous differential equation involves terms up to the second derivative of a function. For the case of constant multipliers, The equation is of the form and can be solved by the substitution The solution which fits a specific physical situation is obtained by substituting the solution into the equation and evaluating the various constants by forcing the solution to fit the physical boundary conditions of the problem at hand. Substituting gives which leads to a variety of solutions, depending on the values of a and b. In physical problems, the boundary conditions determine the values of a and b, and the solution to the quadratic equation for λ reveals the nature of the solution. Case I: Two real roots For values of a and b such that Case II: A real double root If a and b are such that Case III: Complex conjugate roots For values of a and b such that The solution to the homogeneous equation is important on its own for many physical applications, and is also a part of the solution of the nonhomogeneous equation. Applications 
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Differential Equation ApplicationsThese are physical applications of secondorder differential equations. There are also many applications of firstorder differential equations. Azimuthal equation, hydrogen atom: Velocity profile in fluid flow. 
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Applications of 1st Order Homogeneous Differential EquationsThe general form of the solution of the homogeneous differential equation can be applied to a large number of physical problems.

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