Category: Student Work (Page 35 of 44)
Problem 2
I don’t know where I’m making a mistake
Problem 3
I followed the hint too but still don’t know where I’m going wrong
Problem 7 and 8
Anyone else knows what the hint means by “Use a substitute variable to replace y in order to make this DE separable”?
Problem 1:
a. $ \frac{d^2 y}{d x^2} + 2 \frac{d y}{d x} \frac{d^3 y}{d x^3} + x = 0 $
Isolating highest order,
$ y”’ = \frac{y”}{2y} – \frac{x}{2y} $
3rd order
b.$ y” – 3y’ + 2y = x^7 $
Isolating highest order,
$ y”= 3y’ -2y+x^7 $
2nd order
c. $ y’ – y^7 = 0 $
Isolating highest order
$y’ = y^7 $
1st order
d. $ y”y – (y’)^2 =2 $
Isolating highest order,
$ y” = \frac{2}{y} + \frac{(y’)^2}{y} $
2nd order
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