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dy/dx=(x^2+y^2+1)/2xy

dy/dx=(x^2+y^2+1)/2xy

Grade:12

4 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
6 years ago
Hi,

This is a Homogeneous differential equation.
So put y=vx and solve, ie keeping v as avariable find dv/dx in terms of dy/dx and substitute also substitute the value of y in the expression. Upon simplification u will see that the v terms and x terms are segrigated by themselves.

Dont forget to do the back substitution, ie putting y instead of v.
swami iyer
25 Points
3 years ago
No you’re wrong dude.. You can’t substitute y = vx because of that 1 in the numerator! God knows how you made it to IIT geez
swami iyer
25 Points
3 years ago
Instead follow this method,
Substitute y^2 = u and solve, ie keeping u as a variable find du/dx in terms of dy/dx and substitute  also substitute the value of y in the expression.
sandeep
15 Points
2 years ago
Ans. dy/dx = (x^2+y^2+1)/2xy
       y^2 = v.
      2ydu/dx = dv/dx
      ydu/dx = (x^2+v+1)/2x
     (dv/dx)/2 = (x^2+v+1)/2x
       xdv = (x^2+v+1)dx
      (xdv-vdx)/x^2 = (x^2dx + dx)x^2
      y^2-x^2+1 = cx

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