differnation: if y=1/x² show that y d²y/dx² +(dy/dx)² -10y³=0

[markosheehan]

differnation: if y=1/x² show that y d²y/dx² +(dy/dx)² -10y³=0

if y=1/x² show that y d²y/dx² +(dy/dx)² -10y³=0 i can work out y′=-2x^-3 and y″=6x^-4 but when i sub these in i cant make the whole expression equal zero

 

[ecoo]

Keep in mind that y can also be substituted.

 

[stapel]

If y=1/x², show that y d²y/dx² +(dy/dx)² -10y³=0.

I can work out y′=-2x^-3 and y″=6x^-4, but when I substitute these in, I can't make the whole expression equal zero.

Please reply showing your work, including where you plugged "1/x²" in for "y". Thank you!