Math 225 Differential Equations Notes Chapter 2
Math 225 Differential Equations Notes Chapter 2
Math 225 Differential Equations Notes Chapter 2
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Example 10: Solve<br />
dy<br />
dx − 5y = −5 2 xy3<br />
Solution:<br />
This is a Bernoulli equation with n = 3, P (x) = −5, and Q(x) =<br />
−5x/2 So as described before divide by y 3<br />
y −3dy<br />
dx − 5y−2 = − 5 2 x<br />
Now make the substitution v = y 1−3 = y −2 and dv/dx = −2y −3 dy/dx<br />
− 1 dv<br />
2 dx − 5v = −5 2 x<br />
dv<br />
+ 10v = 5x<br />
dx<br />
So now we can use integrating factors to get.<br />
Substituting v = y −2 we get<br />
v = x 2 − 1 20 + Ce−10x<br />
y −2 = x 2 − 1 20 + Ce−10x<br />
How about the solution y = 0 for all x<br />
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