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May 15th, 2019, 11:29 PM  #1 
Member Joined: Apr 2017 From: India Posts: 76 Thanks: 0  Number of constants in general solution
The number of arbitrary constants in the general solution of the differential equation will be 3 or 6? 
May 16th, 2019, 03:58 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
Since this is a third order differential equation, You have to provide one arbitrary constant for each integration needed to solve the equation so there are three. The cube of the first derivative is probably confusing you, but whatever the power of dy/dx it is still only a first derivative so one only gets one arbitrary constant. Do you understand the terms order and degree for a differential equation? The order (which controls the constants) is the order of the highest derivative, regardless of its power. The degree is the highest power of a function of x, in this case also 3 so this is a third degree equation. I hope this image was not sent from a phone in your exam. Last edited by skipjack; May 16th, 2019 at 07:52 AM. 
May 16th, 2019, 06:54 AM  #3 
Member Joined: Apr 2017 From: India Posts: 76 Thanks: 0  No, I sent it from the last year question papers. My exam is on 20th. Thank you for the answer. 

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constants, general, number, solution 
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