MATH 2574H Lecture 12: Lecture 1242014.pdf
Document Summary
You"re given general sol"n form, find the constant by using some initial condition. How to interpret description of diff eq in a mathematical eqn. Use math to find sol"n to diff eq. Tells us more about the real world system. Today: simple ordinary (diff eq is in 1 variable) diff eq of the form y(n) = f(x) where y(n) is the nth derivative of y (dny/dxn) Example: dy/dx = y" = 2x + 1 y(0) = 5. Note: right hand side of diff eq only depends on x. In this case, we can integrate both sides with respect to x. Integrate[y"dx] = integrate[(2x+1)dx] y(x) = x2 + x + c -->general sol"n. Use initial condition y(0) = c = 5 => c = 5 y(x) = x2 + x + 5. If look at general sol"n, it = family of sol"ns. Choose 1 specific curve -->particular sol"n satisfying y(0) = 5.
