anonymous
  • anonymous
solve sqrt(y)dx+(1+x)dy=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
sqrt(y)/dy=-(1+x)/dx
anonymous
  • anonymous
then integrate
Owlcoffee
  • Owlcoffee
\[\sqrt{y} dx +(1+x)dy=0\] You can start off by dividing both sides by "dx": \[\frac{ \sqrt{y} dx +(1+x)dy }{ dx }=\frac{ 0 }{ dx }\] \[\sqrt{y}\frac{ dx }{ dx }+\frac{ dy }{ dx }(1+x)=0\] \[\frac{ \sqrt{y} }{ dy }=\frac{ -(1+x) }{ dx }\] Now, integrating both sides: \[\int\limits \sqrt{y} \frac{ 1 }{ dy }= \int\limits -(1+x)\frac{ 1 }{ dx }\]

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anonymous
  • anonymous
how can i integrate that
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle \sqrt{y}dx+(1+x)dy=0 }\) \(\large\color{black}{ \displaystyle \sqrt{y}dx=-(1+x)dy }\) \(\large\color{black}{ \displaystyle \sqrt{y}\frac{dx}{dy}=-(1+x) }\) \(\large\color{black}{ \displaystyle \frac{1}{-(1+x)}\frac{dx}{dy}= \frac{1}{\sqrt{y}}}\) integrate both sides with respect to y.
anonymous
  • anonymous
left side is same just no dx/dy right
SolomonZelman
  • SolomonZelman
when you integrate the left side with respect to y, the *dy*s are going to cancel.
SolomonZelman
  • SolomonZelman
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SolomonZelman
  • SolomonZelman
hen solve for y. Algebraic task...

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