A curve passes through the point ????0, 5???? and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve…

Question

asked Aug 27, 2020 140k views

1 Answer

Pretty · Answer 1 · 2020-09-03T03:19:34+0000

Answer:
y=2x^2

Explanation:

Given Curve passes through
$\left ( 0,5\right )$

Also the slope of the curve at every point p is twice the Y-coordinate of p

Let the coordinate of p be
$\left ( x,y\right )$

Therefore

$\frac{\mathrm{d} y}{\mathrm{d} x}=2y$

(dy)/(y)=2dx

Integrating both sides

$\int (dy)/(y)=\int 2dx$

$\ln y=2x+c$

Substituting values

$\ln 5=c$

$\ln (y)/(5)=2x$

y=2x^2