Question

Find a second order differential equation where solution is

x^2+y^2+2ax+2by=0

anyone solve please !

Answer 1

Step-by-step explanation:

x2+y2+2ax+2by+c=0⋯(1)

Differentiate w.r.t x

2(x+yy1)+2(a+by1)=0

or x+yy1+(a+by1)=0⋯(2)

Again

differentiate w.r.t. x

1+yy2+y12+by2=0⋯(3)

Differentiate (3) w.r.t. x

yy3+y1y2+2y1y1+by3=0⋯(4)

Eliminating b between (3) and (4), we get yy3+3y1y21+yy2+y12=−by3−by2=