Solve the differential equation `[(e^(-2sqrt(x)))/(sqrt(x))-y/(sqrt(x))](dx)/(dy)=1(x!=0)`

Explanation

Given differential equation is :
`(e^(-2sqrt(x))/(sqrt(x))-(y)/(sqrt(x)))(dx)/(dy)=1`....`(1)`
`implies(dy)/(dx)=(e^(-2sqrt(x)))/(sqrt(x))-(y)/(sqrt(x))implies(dy)/(dx)+(1)/(sqrt(x))y=(e^(-2sqrt(x)))/(sqrt(x))`.............`(2)`
Comparing with the differential equation `(dy)/(dx)+Py=Q`,
`P=(1)/(sqrt(x))`, `Q=(e^(-2sqrt(x)))/(sqrt(x))`
`:. I.F.=e^(int(1)/(sqrt(x))dx)impliesI.F.=e^(2x^(1//2))=e^(2sqrt(x))`
Therefore, the general solution of the given differential equation is
`y*I.F.=intQxxI.F.dx+C`
`impliesye^(2sqrtx)=inte^(2sqrt(x))xx(e^(-2sqrt(x)))/(sqrt(x))dx+C`
`impliesye^(2sqrt(x))=int(1)/(sqrt(x))dx+Cimpliesye^(2sqrt(x))=2sqrt(x)+c`