Transcript Document

Separable Variables
Ex. Solve
dy
dx
 x 3
2
A first-order DE is called separable if it can
dy
be written dx  f  x  g  y 
• To solve these, we’ll isolate the variables.
• Treat
dy
dx
like a fraction.
dy
y
Ex. Solve

dx 1  x
dy
Ex. Solve
 3y
dx
dy  x

, y  4   3
Ex. Solve the IVP
dx
y
Ex. Solve the IVP
dy
2y
y
 e  y  cos x dx  e sin 2 x, y  0   0
If we are asked to find an antiderivative that
we can’t do by hand, we need to express
the answer as an integral function.
dy
 x2
 e , y  3  5
Ex. Solve the IVP
dx
This is called a nonelementary function.
When we divide both sides of the equation,
we may lose a solution where the divisor is
zero.
dy
2
Ex. Solve
 y 4
dx
Did we lose any solutions? Are they particular or singular?
Your first test of the semester will
be on Wednesday.