PennyGirl said:so...
integrating once...
x'=.0345*x^-2*t
then again...
x=.0345/2*x^-2*t^2+C\
?
NO. You cannot separate a second derivative like this. A second derivative cannot be treated like a fraction.PennyGirl said:d^2 X * X^2 = .5 dt^2
integrate both sides...
dx * x^3/3=(.5*t + C) *dt
at t=0, dx/dt=0 and x=10...
0*10^3/3 = .5*0 + C
C=0
dx * x^3/3 = .5*t*dt
integrate both sides again...
x^4 / 12 = .25*t^2 + C
same refs...
10^4/12 = .25*0 +C
C = 833.3
x^4/12 = .25*t^2 + 833.3
algebra...
x= (3*t^2 + 10000)^(1/4)
but that doesn't work...
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives, or rates of change, to model and predict the behavior of a system over time.
There are several types of differential equations, including ordinary differential equations, which involve a single independent variable, and partial differential equations, which involve multiple independent variables. Other types include linear and nonlinear, first-order and higher-order, and homogeneous and non-homogeneous differential equations.
Differential equations are used to model and analyze a wide range of phenomena in science and engineering, including physical systems, chemical reactions, biological processes, and economic systems. They are also essential in fields such as physics, engineering, and economics for making predictions and solving problems.
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