Differential Equations help!

[MeENCaNTaMiDiTa]

I have two quick problems that i cannot remember how to do the first one is this:

Use integration to find a general solution of the differential equation.

dy/dx=x(x+3)^(1/2) or just x multiplied by the square root of (x+3)

the answer should end up being: (2/5)(x-3)^(5/2) + 2(x-3)^(3/2) + C


the other question i had was this one:

Find the general solution of the differential equation.
(2+x)(dy/dx) = 3y

Thanks so much for any help!

 

[Unco]

G'day,

For the first one: integrate both sides with respect to x straight off. The substitution u=x+3 may help.

For the second one: separate variables by dividing both sides by (2+x) and by 3y. Then integrate both sides with respect to x, remembering the integral of 1/x is ln|x|.

See how you go.

 

[Daniel_Feldman]

Just building on what Unco said, if u=x+3, remember that x=u-3. Using this could also prove useful.