CHAPTER 46
Differential Equations
46.1
Solve
The variables are separable: 7y dy = 5x dx. Then, J ly dy = J 5x dx,
Here, as usual, C represents an arbitrary constant.
46.2
Solve
46.3
Solve
46.4
Solve
46.5
Solve
solution.
Separate the variables.
431
46.9
Solve
46.8
Solve
46.7
Solve
46.6
Solve
If we allow C to be negative (which means allowing C l to be complex),
Hence,
Taking reciprocals, we get
Note that y = Ce" '
2 is a general
of the form y = Ce
kx
is a solution.
Separate the variables.
In | y | = kx + C,, \ y \ = e
k *
+c > = e
Cl • e
1 " = C 2 e
kx . Any function
The variables are separable.
7 In |y| =51n|jt| + C I ,
e 5 ( in M+c,)/7 = gCl . e scin Mjn | y | = C 2 \ x \
s '\ where C 2 = e
c
' >0. Note that any function of the form y =
Cc
5 '
7
satisfies the given equation, where C is an arbitrary constant (not necessarily positive).