4. Linear DEs of Order 1
If P = P(x) and Q = Q(x) are functions of x only, then
is called a linear differential equation order 1.
We can solve these linear DEs using an integrating factor.
For linear DEs of order 1, the integrating factor is: e∫Pdx
The solution for the DE is given by multiplying y by the integrating factor (on the left) and multiplying Q by the integrating factor (on the right) and integrating the right side with respect to x, as follows:
Example 1:
Solve 
Example 2:
Solve 
Example 3:
Solve 
Example 4:
Solve 2(y - 4x2)dx + x dy = 0
Example 5:
Solve 
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