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The university of wales, aberystwyth - institute of mathematics & physics exam for differential equations (ma11210) held in june 2008. The exam consists of multiple-choice questions related to the order, degree, and linearity of differential equations, as well as finding their general solutions. The document also includes problems on separating variables, using integrating factors, and solving specific differential equations.
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Full marks will be given for complete answers to all questions in Section A and to three questions in Section B. In Section B, credit will be given for the best three answers.
Calculators must not be used in this examination.
Section A
a) 1
x
xy dx
dy x.
b) 2 2 1
2
d y .
c) 2 1
2 2
2 +^ =
dy dx
d y .
d) 2 1
2
2
2 + +^ =
y dx
dy dx
y
d^.
e) 2 4
2 2 xe y x dx
y (^) x
e cos x dx
dy (^) x = 2 −^2 +. [5]
dx x ( x )
dy
, x > 0. [5]
dy 1 + x^3 =^2 is valid for x > 0. By separation of
variables, or otherwise, find the solution that satisfies y ( 1 ) = 2.
t
( ) ( )
may be transformed into a linear first-order equation for the new dependent variable
Find the solution of the differential equation: 1
for which y = 0 when x = 0. [8]
