Question

solve sqrt(y)dx+(1+x)dy=0

Answer 1

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

Answer 2

then integrate

Answer 3

\[\sqrt{y} dx +(1+x)dy=0\]
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:
\[\int\limits \sqrt{y} \frac{ 1 }{ dy }= \int\limits -(1+x)\frac{ 1 }{ dx }\]

Answer 4

how can i integrate that

Answer 5

\(\large\color{black}{ \displaystyle \sqrt{y}dx+(1+x)dy=0 }\)

\(\large\color{black}{ \displaystyle \sqrt{y}dx=-(1+x)dy }\)

\(\large\color{black}{ \displaystyle \sqrt{y}\frac{dx}{dy}=-(1+x) }\)

\(\large\color{black}{ \displaystyle \frac{1}{-(1+x)}\frac{dx}{dy}= \frac{1}{\sqrt{y}}}\)

integrate both sides with respect to y.

Answer 6

left side is same just no dx/dy right

Answer 7

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