## anonymous one year ago solve sqrt(y)dx+(1+x)dy=0

1. anonymous

sqrt(y)/dy=-(1+x)/dx

2. anonymous

then integrate

3. 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: $\int\limits \sqrt{y} \frac{ 1 }{ dy }= \int\limits -(1+x)\frac{ 1 }{ dx }$

4. anonymous

how can i integrate that

5. 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.

6. anonymous

left side is same just no dx/dy right

7. SolomonZelman

when you integrate the left side with respect to y, the *dy*s are going to cancel.

8. SolomonZelman

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9. SolomonZelman

hen solve for y. Algebraic task...

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