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S
 4 years ago
use separation of variables to solve differential equation :dy/dx=t/(y+1)^(1/2) , y(1)=3 ?
S
 4 years ago
use separation of variables to solve differential equation :dy/dx=t/(y+1)^(1/2) , y(1)=3 ?

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.Sam.
 4 years ago
Best ResponseYou've already chosen the best response.1multiply both sides by\[\sqrt{y+1}\] Then integrate \[\frac{dy}{dx} \sqrt{y+1}\text{ = }t\] \[\sqrt{y+1}dy=tdx\] \[\int\limits_{}^{}\sqrt{y+1}dy=\int\limits_{}^{} tdx\]

S
 4 years ago
Best ResponseYou've already chosen the best response.0I got this part, but I am confused how to solve it

.Sam.
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits \sqrt{y+1} \, dy=\frac{2}{3} (y+1)^{3/2}\] \[\int\limits_{}^{}tdx=tx+c\]  \[\frac{2}{3} (y+1)^{3/2} =tx+c\] \[(y+1)^{3/2}=\frac{3(tx+c)}{2}\] \[y+1=(\frac{3(tx+c)}{2})^{2/3}\] \[y=(\frac{3(tx+c)}{2})^{2/3}1\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I think it's supposed to be dy/dt ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then it's 2/3*(y+1)^(3/2) = (t^2)/2 +C

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0use I.V. to find C , solve for y(t)
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