wezzo62 said:Find the general solution to: dy/dx = 3x2y
I tried saying u = 3x2 and v = y
then du/dv = 6x and dv/dy = 1
and get 3x2 + 6xy but now i think iv gone completely the wrong way around this . . . .
Differential equations are mathematical equations that describe how a quantity changes over time, based on the rate of change of that quantity. They are commonly used in physics, engineering, and other fields to model real-world phenomena.
Differential equations are important because they allow us to understand and predict the behavior of complex systems. They are used in a wide range of applications, from predicting the movement of planets to designing electrical circuits.
There are several methods used to solve differential equations, including separation of variables, substitution, and integrating factors. Numerical methods, such as Euler's method and Runge-Kutta methods, can also be used to approximate solutions.
No, not all differential equations can be solved analytically. Some equations are too complex and have no known closed-form solution. In these cases, numerical methods are used to approximate the solution.
Solving differential equations has a wide range of applications, including predicting the behavior of physical systems, designing control systems, and understanding population dynamics. It is also used in many fields of science and engineering, such as mechanics, thermodynamics, and electrical engineering.