Differential equations - finding constants

[shinobiazra]

Find values of the constants a and k so that y(x) = ax^k solves the differential equation;

(dy/dx)^2 + [(3y^2)/(x^2)] + [(2y)/(x^4)]


I tried substituiting ax^k into the DE but it did not work. I need to separate x and y but I cannot do it then I need to integrate it I think. I just don't know how to go about this question.

HELP!

 

[elibj123]

I see no equation, only an expression. I guess you mean that this expression equals zero?

Please show what you've done so far with substitution

 

[tiny-tim]

Hi shinobiazra!

(try using the X² tag just above the Reply box )

I tried substituiting ax^k into the DE but it did not work. I need to separate x and y but I cannot do it then I need to integrate it I think.

No, there's no integration, all you need to do is differentiate.

If y = ax^k, what is dy/dx? ​