Summary Separable Differential Equations | Calculus II Notes
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Module
Math 112 (MATH112)
Institution
University Of The Fraser Valley (UFV)
Defines differential equations, gives step by step examples on how to soble separable differential equations (both general and particular solutions) and initial conditions,
2.4 Separable Differential Equations
an equation involving a function and some of its derivative is called a differential equation
the order of a differ, is the order ofthe heighest derivative equation
appearing in the
eg.
f" f
(x): (x) is a fourth order
solving a
differ find all functions thatsatisfy the equation.
example:y':f(x)
y Sf(x)dX
=
=x 2
y
y
(x'dx
=
=
c
+
there are many solutions depending on the C value
for a particular solution pick outa Cvalue of specify a
pointon y= f(x), or specify a value on f
example:
findy, x2
y (1)
3
y' and
= =
firstsolve the integral
y (x'dx
c
2
= +
=
the solve for cat y(1) 3
=
bz c 3
+
=
C 3 =
-
1z 8/3
=
y x3x 83
+
=
specifying a value off is called an initial condition
first order separable diff.egs.
form: f(x). g(y)
1
=
steps to solve:
1)"separate"the variables
giys dy f(x)dx
=
-)
integratebedee
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