One of the following is a general solution of the homogeneous differential equation y" - 5y + 6y = 0 y = ae +be 2z y = ae" + be2z y = ae? + be 2z y = ae + be2 and one of the following is a solution to the nonhomogeneous equation y" - 5y' + 6y = -6e y = 12e y = -9e? 6e y = y = -3e? By superposition, the general solution of the equation y"-5y' + 6y = -6e is Find the solution with y(0) = 5 y' (0) = 3 Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be The fundamental theorem tells me that that this is the unique solution to the IVP on the interval

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.