Download 6.2 Differential Equations

6.2 Differential Equations
6.3 Separation of Variables
Solving a Differential Equation
• Solve the differential equation:
2x
y' 
y
Solving a Differential Equation
dy
2
  xy 
dx
Separation of Variables
• Find the general solution:
 x 2  4
dy
 xy
dx
Finding a Particular Solution
• Given the initial condition y(0)=1, find the
particular solution of the equation:
xydx  e
 x2
2
y
 1 dy  0
Finding a Particular Solution Curve
• Find the equation of the curve that passes
through the point (1,3) and has a slope of
y
x2