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Explanation & Answer
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Running head: APPLIED MATHEMATICS
Applied Mathematics
Student’s Name
Institution Affiliation
1
APPLIED MATHEMATICS
1. dy/dx= -x(y2+y),
2
y(2) =1
Putting like terms together
dy/ (y2+y)= (-x)dx
Integrate
∫dy/(y2+y) = ∫dx(-x)
Thus, 1/-y+ ln(y) = ln(x)+c
So, y(x) = 1/(ln(x)+c
Applying y(2) = 1 we obtain
1= y(2) = 1/(ln2+C)
1= 1/(ln2+C)
ln2 +C=1
C= -0.693147
Finally,
y(x) = 1/(ln(x)-0.0693147
2. xy’+2y=8x2, y(1)=3
xy’+2y =8x2
dy/ dx + 2y/x =8x------(1)
Comparing with the standard form dy...
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