Marc L. answered • 11/27/20

Helping others understand things one step at a time

I'm going to define y' as dy/dx, now lets start by taking the first derivative:

~~8~~y'/(~~8~~y)=5y+5xy', y'-5xyy'=5y^{2}, y'(1-5xy)=5y^{2}, y'=5y^{2}/(1-5xy)

now lets let y'' be d^{2}y/(dx^{2}) and take the second derivative:

y''=((1-5xy)(10yy')-(5y^{2})(5y+5xy'))/(1-5xy)^{2}

Now wherever you see a y', replace it with the equation we had above y'=5y^{2}/(1-5xy):

**y''=((1-5xy)(10y(5y**^{2}**/(1-5xy)))-(5y**^{2}**)(5y+5x(5y**^{2}**/(1-5xy))))/(1-5xy)**^{2} (I will leave the simplifying to you)

there is your second derivative

now for part b) set y''=0 and solve for the values of x and y that satisfy that equation