Question

Please help with some questions on differential equations! (see attached)

Answer 1

I specifically need help with question 15, 16 and 17. Thanks!

Answer 2

I have no idea how to do 15, but I'll post my process for 16...

Answer 3

16. P(1)=2
\[\frac{ dP }{ dt } = \sqrt{Pt} \]
\[\int\limits_{}^{} P^{-1/2} dP = \int\limits_{}^{} t^{1/2} dt\]
\[2p^{1/2} = \frac{ 2 }{ 3 } t^{3/2} + c\]
\[2(2)^{1/2} = \frac{ 2 }{ 3 } + c\]
\[c=2\sqrt{ 2 } - \frac{ 2 }{ 3 }\]

However, Wolfram Alpha gives a very different answer: http://www.wolframalpha.com/input/?i=p%27%3Dsqrt%28pt%29

Answer 4

this is a separable diff equation

Answer 5

so solve for P in your equation

Answer 6

2* P^(1/2) = 2* t^(3/2) + c , solve for P

Answer 7

divide both sides by 2 ,
P^(1/2) = t^(3/2) + C , where C = c/2, still just a constant

Answer 8

woops,

Answer 9

P^(1/2) = 1/3*t^(3/2) + C , now square both sides
P = ( 1/3 t^(3/2) + C ) ^2

Answer 10

P = 1/9 t ^3 + 2*1/3*C*t^(3/2) + C^2

Answer 11

are you still there?

Answer 12

Yeah I'm just writing my answer. Thanks alot! But can you help me with the other two as well?