Final answer:
The request seems to mix different mathematical problems with incomplete information, making it impossible to provide a solution. To solve differential equations using undetermined coefficients, it is necessary to clarify and provide the full equation. The text references a variety of mathematical concepts without sufficient information to provide accurate assistance.
Step-by-step explanation:
The request contains several parts of questions related to solving differential equations and other mathematical problems. The initial request to solve a differential equation by undetermined coefficients cannot be fulfilled as it appears there are typos in the provided equation, making it unclear. Similarly, other equations and problems mentioned are either incomplete or lack context for a solution. It would be best to clarify and provide the correct mathematical problems or equations in full to receive accurate assistance.
For solving differential equations by the method of undetermined coefficients, a common approach is to first find the complementary solution to the homogeneous differential equation, then propose a particular solution based on the form of the nonhomogeneous term, and adjust the coefficients to satisfy the original differential equation.
The provided text also references to various mathematical concepts such as quadratics, derivatives, logarithmic curves, wave functions, Heisenberg's uncertainty principle, and tension in strings. This highlights the broad range of topics in mathematics from algebra, calculus, to physics applications.