Question

Use the concept that y = c, -∞ < x < ∞, is a constant function if and only if y' = 0 to determine whether the given differential equation possesses constant solutions and find them if they exist. (Enter your answers as a comma-separated list. If there are no constant solutions, enter NONE.) 4xy' + 5y = 15 

          Use the concept that 
y = c, -∞ < x < ∞,
 is a constant function if and only if 
y' = 0
 to determine whether the given differential equation possesses constant solutions and find them if they exist. (Enter your answers as a comma-separated list. If there are no constant solutions, enter NONE.)
4xy' + 5y = 15
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Added by Kristina J.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Use the concept that y = c, -∞ < x < ∞, is a constant function if and only if y' = 0 to determine whether the given differential equation possesses constant solutions and find them if they exist. (Enter your answers as a comma-separated list. If there are no constant solutions, enter NONE.) 4xy' + 5y = 15
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Transcript

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00:01 Hello everyone, so here it is given that y x is equal to x to the power.
00:04 So derivative of this y -dash is equal to n x to the power n minus 1 and double derivative of this will be n -minus 1 x to the power n minus 2.
00:15 So we will get substituting the original equation we will get x square n -1 x -n minus 2 x to the power n -2 minus x -n minus x -n minus 1 minus 8 x -n is equal to 0.
00:29 So x to the power n, n square minus n minus n minus 8 is equal to 0.
00:36 So x to the power n square 2n minus 2n minus 8 is equal to 0.
00:46 So x not equals to 0...
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