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

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

S Group TitleBest ResponseYou've already chosen the best response.0
I got this part, but I am confused how to solve it
 one year ago

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

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
I think it's supposed to be dy/dt ?
 one year ago

S Group TitleBest ResponseYou've already chosen the best response.0
oops, yes, thats dy/dt
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
then it's 2/3*(y+1)^(3/2) = (t^2)/2 +C
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
use I.V. to find C , solve for y(t)
 one year ago
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