The differential equation `y(dy)/(dx)+x=C` represents
The differential equation `y(dy)/(dx)+x=C` represents
A. family of hyperbolas
B. family of parabolas
C. family of ellipses
D. family of circles
4 views
1 Answers
Given, that `y(dy)/(dx)+x=C`
`Rightarrow y(dy)/(dx)=C-x`
`Rightarrow ud y=(C-x)dx`
On integrating both sides, we get
`(y^(2))/(2)=Cx-(x^(2))/(2)+K`
`Rightarrow (x^(2))/(2)+(y^(2))/(2)=Cx+K`
`Rightarrow (x^(2))/(2)+(y^(2))/(2)=Cx+K`
`Rightarrow (x^(2))/(2)+(y^(2))/(2)=Cx=K`
Which represent family of circles.
4 views
Answered