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Differential Equations

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Moderate

Number of Conditions to Yield a Unique Solution

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Usually, given a differential equation, there are many solutions. We need some conditions to determine the solution uniquely. Meanwhile, if the conditions are not imposed correctly, there may be no solutions. For the following equations and the given sets of conditions, determine which can't yield a solution uniquely. ​

Select all that apply.

A

A suitable condition for $y'-2xy=3x$ is

$y(0)=3$

B

A suitable condition for $y''-2xy=3x$ is

$y(0)=3$

C

A suitable set of conditions for $y''-2xy=3x$ is

$y(0)=3$
$y'(0)=1$

D

A suitable set of conditions for $y''-2xy=3x$ is

$y(0)=3$
$y(1)=1$

E

A suitable set of conditions for $y''-2xy=3x$ is

$y(0)=3$
$y'(0)=1$
$y(1)=1$