Find the general solution of the differential equation. Use C for the constant of integration.

Question

Find the general solution of the differential equation. Use C for the constant of integration.
dy/dx= 10x + (7/x)

 

So I tried this problem a couple times and got it wrong. My best attempt is as follows:

5x^2 +(7x/(x^/2))

 

What am I doing wrong. I have a felling it has something to do with the 7/x part because I don't understand how to integrate those. Please help me.

Answer 1

dy/dx = 10x+7x^-1

 

y = 10x² /2 - 7ln|x|  + c

 

y = 5x²  - 7ln|x| + c

 

 

Answer 2

dy/dx = 10x + 7x^-1

 

 

To find the function y, simply take the anti-derivative  of dy/dx using the power rule.

 

y = 5x² + 7lnx + C

 

 

Note: Your first term in the integration was correct.  When taking the integral of N/x, the integral is always Nlnx by rule.