Question

dy/dx=2x/5y y=1 x=0

Answer 1

\(\large\color{slate}{ \displaystyle \frac{dy}{dx}=\frac{2x}{5y} }\) if `y=1` and `x=0`


\(\large\color{slate}{ \displaystyle \frac{dy}{dx}=\frac{2(0)}{5(1)}=0 }\)

Answer 2

5y dy=2x dx
integrating
\[5\int\limits y~dy=2 \int\limits x~dx\]
\[5\frac{ y^2 }{ 2 }=2 \frac{ x^2 }{ 2 }+c\]
when x=0,y=1
\[\frac{ 5 }{ 2 }=0+c,c=\frac{ 5 }{ 2 }\]
\[5\frac{ y^2 }{ 2 }=x^2+\frac{ 5 }{ 2 }\]
\[5y^2=2 x^2+5\]