No, you don't obtain that equation. If u= t^2, then dx/dt= dx/du du/dt=2t dx/du.nocloud said:i have this equation:
dx/dt = t/(x*t^2+x^3)
using the substitution u = t^2, i obtain the following equation:
du/dx = 2u/(ux+x^3)
does anybody know how i can solve this equation?
Differential equations are mathematical equations that relate a function with its derivatives. They are used to model many real-world phenomena, such as growth and decay, motion, and electrical circuits.
Ordinary differential equations involve a single independent variable, while partial differential equations involve multiple independent variables. Ordinary differential equations are used to model phenomena that change over time, while partial differential equations are used to model phenomena that vary over space.
Differential equations can be solved through analytical methods, such as separation of variables or using integrating factors. They can also be solved numerically using methods such as Euler's method or Runge-Kutta methods.
Differential equations have a wide range of applications in physics, engineering, economics, and biology. They are used to model population growth, heat transfer, fluid dynamics, and many other phenomena.
Yes, there are many real-life examples of differential equations. Some common examples include the motion of a pendulum, the spread of diseases in a population, and the cooling of a cup of coffee. Differential equations are also used in engineering to design bridges, airplanes, and other structures.