I.
React on the
following statements. (4 points each)
1. The
primitive solution associated with y = Cx2 + C2
has a degree of 1.
2. The
equation y – ex =
0 is a solution of y’ =
-y2.
3. The
equation y =
5e
–x is
a solution of y’ +
y = 0
on the interval (-
0].
0].
4. The
function of g(x,y) =
x3
is homogeneous with order 
.
is homogeneous with order .
5. The
differential equation dt – 
dy
= 0 is exact when v
denotes an arbitrary constant not parameter.
dy
= 0 is exact when v
denotes an arbitrary constant not parameter.
II.
Show your
solution to the following:
1. Obtain
the differential equation of family of circles with fixed radius r
and tangent to x-axis.
Draw the diagram that it represents and determine the order, degree, linearity
and independent variable(s) of the resulting differential equation. (10 points)
2. Test
the exactness for (2xy –
tan y)dx +
(x2 – xsec2
y)dy =
0. If exact, use Partial Derivatives using two ways. (15 points)
3. Find
the general solution of the differential equation (x + b)y’ =
ax – ny
such that a, b, n
are constants with n 
0, n -1, a linear differential equation of order
one. (20 points)
0, n -1, a linear differential equation of order
one. (20 points)
4. Show
that equation (xnyn+1
+ ax)dy +
(xn+1yn
+ ay)dx =
0 if n 0 1, can be solved using integrating factor
found by inspection. (20 points)
0 1, can be solved using integrating factor
found by inspection. (20 points)
5. Using
determination of integrating factor, find the solution for (2y2 +
3xy –
2y +
6x)dx + x(x +
2y –
1)dy = 0.
(15 points)
Anung sagot sa test number 2
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