# Characteristics of an equation

• Jan 7th 2010, 09:41 AM
davefulton
Characteristics of an equation
How do I calculate the slope of an equation if I don't have any initial data?

du/dt + (1/2 * (1 + u)^2) = 0

The slope is therefore

dx/dt = a(u) = f'(u) = 1 + u

With no initial data how do I calculate u(x,t)?
• Jan 9th 2010, 01:58 PM
Henryt999
Solve for slope without data?
Calculating anything without initial data is veeeeeery troublesome =)

du/dt + 1/2*(1+u)^2 = 0

du/dt+ 1/2*(1^2+2u+u^2) = 0

du/dt +1/2 + u + u^2 = 0

du/dt + u = -u^2 - 1/2 this gives you ke^-x

Set
\$\displaystyle u = ax^2 + bx + c \$ gives you uŽ= 2ax +b

\$\displaystyle 2ax +b +ax^2 +bx +c = -u^2 -1/2\$ gives you a = -1
\$\displaystyle

2ax +bx = 2*(-1) +b = 0
\$ b = 2

\$\displaystyle b + c = -1/2\$ gives you c = -2,5

\$\displaystyle U = Ke^(-x) -x^2 +2x -2.5\$

To determine K, I think you need a value somewhere,
If you plot that graph for different values of K you will see that the slopes have different angles exept for the x value for maximum/minimum point, is that the value you are trying to find? Otherwise you need some initial data to determine K. ( I think)