Answer:[tex]y=2x^2[/tex]
Step-by-step explanation:
Given Curve passes through [tex]\left ( 0,5\right )[/tex]
Also the slope of the curve at every point p is twice the Y-coordinate of p
Let the coordinate of p be[tex] \left ( x,y\right )[/tex]
Therefore
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=2y[/tex]
[tex]\frac{dy}{y}=2dx[/tex]
Integrating both sides
[tex]\int \frac{dy}{y}=\int 2dx[/tex]
[tex]\ln y=2x+c[/tex]
Substituting values
[tex]\ln 5=c[/tex]
[tex]\ln \frac{y}{5}=2x[/tex]
[tex]y=2x^2[/tex]
