#4 apply an appropriate variable substituion to solve the differential equation:

ID: 3345947 • Letter: #

Question

apply an appropriate variable substituion to solve the differential equation:

y^2 y" = y'

for its general solution function y=y(x)

#5 solve the differential equation

y'y'' = 4x

with the initial conditions y(1) =5 and y'(1) =2

#6 find two power serires solutions about the point x = 0 for the differential equation:

y'' - xy' + 2y = 0

for each series, unless its terminates, find the first 4 non-zero terms

#7 find two power serires solutions about the point x = 0 for the differential equation:

(x^2 + 1)y'' + 2xy' = 0

for each series, unless terminats, find the firs 4 none-zero terms

y''y' = 4x

(y') ^2 = 4x^2 + c at x=1 y'=2 so c= 0

y'(x) = (+or - )2x + b at x=1 y'=2 so b = 0

y(x) = x^2 + k at x=1 y=5 so k =4

where c b k are constant variable.
y(x) = x^2 + 4

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