Find the General Solution of:

(y) / (d) = e^(-2x)

Explain also.

Thanks

just trying

the given expression can be written as

d(dy)=x(e^-2x)dx

dy=int((x)(e^-2x)dx

by applying by parts

dy=x(e^-2x/-2)-(e^-2x/-2)

y=int(x(e^-2x/-2)+(e^-2x/2))

y=int(x)(e^-2x/-2)+int(e^-2x/2)

in 1st int apply by parts and sec simple int to get general soln

y=x(e^-2x/-2)-(e^-2x/-2)+e^-2x/-4)

d²y/dx² = e^-2x

d(dy/dx) = e^-2x.dx

Integrate both the sides :

dy/dx = -e^-2x/2 + c

dy = (-e^-2x/2 + c)dx

Again integrate both the sides ;

y = e^-2x/4 + cx + d where c and d are the constants of integration.