InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The solution of the differential equation `x(dy)/(dx)+y=x^(3)y^(6)`, isA. `x^(7)=5y^(5)+Cx^(2)y^(5)`B. `2x^(7)=5y^(5)+Cx^(2)y^(5)`C. `5x^(7)=2y^(5)+Cx^(2)y^(5)`D. `2x^(7)=5y^(5)+Cx^(5)y^(2)` |
|
Answer» Correct Answer - B The given differential equation can be written as `(1)/(y^(6))(dy)/(dx)+(1)/(xy^(5))=x^(2)` Let `y^(-5)=v`, Then, `-5y^(-6)(dy)/(dx)=(dv)/(dx)rArry^(-6)(dy)/(dx)=-(1)/(2)(dv)/(dx)` Substituting there values in the given differential equation, we get `-(1)/(5)(dv)/(dx)+(1)/(x)v=x^(2)` `rArr" "(dv)/(dx)-(5)/(x)v=-5x^(2)" ...(i)"` This this the standard form of the linear differential equation having integrating factor `"I.F"=e^(int-(5)/(x)dx)=e^(-5logx)=(1)/(x^(5))` Multiplying both sides of (i) by I.F. and integrating w.r.t. x, we get `v-(1)/(x^(5))=int-5x^(2).(1)/(x^(5))dx` `rArr" "(v)/(x^(5))=(5)/(2)x^(-2)+C` `rArr" "y^(-5)x^(5)=(5)/(2)x^(-2)+C,` which is the required solution. |
|