2. Solve the Differential equation
x 2 y ' 5 xy ' 4 y 0
x 2 y ' 5 xy ' 4 y 0
. 1
The operator form of the differential equation is
d
x 2 D 2 y 5 xDy 4 y 0
D
dx
x D
2
2
5 xD 4 y 0 . 2
Let x e z so that z ln x, x 0 and
d
dz
dz 1
dx x
dy dy dz 1 dy
dx dz d

Find the particular antiderivative F for satisfying the conditions.
through (0.5,7)
Given, f x 2 x 4 x 2
Antiderivative of f x f x dx
2 x 4 x 2 dx
2 xdx 4 x 2 dx
x 2 x 2 1
2 4
C
2 2 1
x 1
x2 4
C
1
x2
4
C
x
4
C.
x
Given F x passes throug

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