- #1
Helios
- 269
- 63
help me solve
( 1 / x^2 ) d / dx [ x^2 ( df / dx ) ] = - f^( 3 / 2 )
I think it needs a series sol'n but it's tough
( 1 / x^2 ) d / dx [ x^2 ( df / dx ) ] = - f^( 3 / 2 )
I think it needs a series sol'n but it's tough
Helios said:help me solve
( 1 / x^2 ) d / dx [ x^2 ( df / dx ) ] = - f^( 3 / 2 )
I think it needs a series sol'n but it's tough
The equation represents a second-order differential equation in which the dependent variable, f, is related to the independent variable, x, and its first and second derivatives.
To solve this equation, you can use the method of separation of variables. First, rearrange the equation to get df/dx on one side and f on the other side. Then, integrate both sides with respect to x and solve for f.
The general solution to this equation is f(x) = C/x, where C is a constant. This solution can be obtained by substituting u = f^(1/2) and solving the resulting first-order differential equation.
Yes, this equation can also be solved using the method of power series. In this method, you assume that the solution can be represented by a power series and then find the coefficients by substituting the series into the equation.
This equation has various applications in physics and engineering, such as in the study of heat transfer, fluid mechanics, and electrical circuits. It can also be used to model natural phenomena, such as population growth or radioactive decay.