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Extra credit problems
5 poits each No partial credit
1. Solve the initial value problem
de = x(y + y) ,
& Solve the initial value problem
xy + 2y = 8x² g (1)=3
3 solve the equation
cg Fy), 3(3)'= 1
A
= =
Y tx
X Х
4. Solve the initial velice problem
by "tyl-y=0 4(0)=-1 , f'(o)= 3
5. Solve the equation
z (4) - 89 +16y=0
6. Solve the eqreation
Y"+2y'-3y = -16x ex
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7. Verify that ye = x² is a solution of
equatici
x ²4" 4x4'+byž o ou (0,oo)
Find second linearly independent
solection,
40-
8, Solve the equation
flott guys -
by of variations of pasuuters
9 Solve the system
علیے
mecens
2x'-5x + y'=0
x' - x +4'
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Explanation & Answer
here it is
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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