Non-Homogeneous Cauchy Euler Differential Equation, CHANGE OF VARIABLE

▼ IMPORTANT ▼
In this video we will see a solved example (solved exercise) of a nonhomogeneous Cauchy Euler linear ordinary differential equation of second order, which can be transformed by substitution (change of variable) into a differential equation of constant coefficients, using exponentials and natural logarithm (another method to solve it is variation of parameters). Once this change of variable has been made, we solve the auxiliary equation or characteristic equation, to obtain the general solution of the related homogeneous equation (complementary solution), and then propose a particular solution (in this case, functions are repeated), derive twice by applying product rule, substitute, simplify by factoring by common factor, equalize the coefficients and solve the algebraic system of linear equations, then we write the general solution for the variable t, and finally we return to the original variable x. Everything explained step by step.
Differential Equations #Cauchy #Euler
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** BIBLIOGRAPHY **
Differential Equations, Edwards and Penney
Differential Equations, Daniel A. Marcus
Differential Equations, Dennis G. Zill
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