Your problem statement is incomplete - it doesn't say what you need to do. Are you supposed to show that the equation with y2 is a solution of the diff. equation?aaronfue said:
"after setting it to zero" - ??aaronfue said:
aaronfue said:
That is possibly a typo in the book. The right side of that equation is the same as c1x + c2, where c2 = (1/4)c12.aaronfue said:
OK, that wasn't clear to me. You could work with the equation as-is, without moving y to the other side. It doesn't make much difference either way.aaronfue said:
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives to express the rate of change of a variable over time.
The purpose of solving a differential equation is to find a function that satisfies the given equation, which can then be used to make predictions and model real-world phenomena.
There are several types of differential equations, including ordinary differential equations (ODEs) that involve a single variable, partial differential equations (PDEs) that involve multiple variables, and stochastic differential equations (SDEs) that involve random variables.
The method used to solve a differential equation depends on its type and complexity. Some methods include separation of variables, substitution, and using integrating factors. Numerical methods, such as Euler's method and Runge-Kutta methods, can also be used to approximate solutions.
Differential equations are used in many fields, including physics, engineering, economics, and biology. They can be used to model population growth, chemical reactions, heat transfer, and electrical circuits, among other things. They also play a crucial role in the development of mathematical models for predicting and understanding various phenomena in the natural world.
