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pat666 said:Thanks Dick,
this question is confusing because x is y. anyway I have
x=sqrt(4t^2+8C)?THANKS
pat666 said:Yes you do, my bad. so it should be ln(x)/4=t^2/2+C
so x=e^(2t^2+4c)??
Differential equations are mathematical equations that describe the relationship between a function and its derivatives. They are used to model a wide range of phenomena in science and engineering.
Differential equations allow us to understand and predict how systems change over time. They are essential for making accurate predictions and optimizing processes in various fields, including physics, biology, and economics.
There are various methods for solving differential equations, depending on the type of equation. Some common techniques include separation of variables, substitution, and using integral transforms. It is also possible to use numerical methods to approximate solutions.
Ordinary differential equations (ODEs) involve a single independent variable, while partial differential equations (PDEs) involve multiple independent variables. ODEs describe the behavior of one-dimensional systems, while PDEs are used to model multi-dimensional systems.
Yes, differential equations have numerous real-world applications. They are used in physics to model motion and describe the behavior of physical systems. In engineering, they are used to design and optimize control systems. They are also used in biology to model population growth and in economics to predict market trends.