InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the particular solution of the differential equation:`(1+e^(2x))dy+(1+y^2)e^x dx=0,`given that `y=1, `when `x=0.` |
|
Answer» Given differential equation is `(1+e^(2x))dy+(1+y^(2))e^(x)dx=0` `implies (dy)/(1+y^(2))+(e^(x)dx)/(1+e^(2x))=0` `impliesint(dy)/(1+y^(2))+int(e^(x)dx)/(1+e^(2x))=C` Let `t=e^(x)impliese^(x)dx=dt` `:.tan^(-1)y+int(dt)/(1+t^(2))=C` `implies tan^(-1)y+tan^(-1)t=C` `implies tan^(-1)y+tan^(-1)e^(x)=C` Now, put `x=0` and `y=1`, `:. tan^(-1)1+tan^(-1)e^(0)=C` `implies(pi)/(4)+(pi)/(4)=CimpliesC=(pi)/(2)` put the value of `C` in equation `(1)`, `tan^(-1)y+tan^(-1)e^(x)=(pi)/(2)` which is the required particular solution. |
|