The solution curve, of the differential equation 2y(dy)/(dx)+3=5(dy)/(dx), passing through…

Question

The solution curve, of the differential equation $2y\frac{dy}{dx}+3=5\frac{dy}{dx}$, passing through the point $(0,1)$ is a conic, whose vertex lies on the line :

Accepted Answer

$\begin{gathered} 2y\frac{dy}{dx}+3=5\frac{dy}{dx} \ 2ydy+3dx=5dy \ {y}^{2}+3x=5y+{c|}_{(0,1)} \ 1+0=5+c \ c=-4 \ {y}^{2}-5y=-3x-4 \ {y}^{2}-5y+\frac{25}{4}-\frac{25}{4}=-3x-4 \ {(y-\frac{5}{2})}^{2}=-3x+\frac{9}{4} \ {(y-\frac{5}{2})}^{2}=-3(x-\frac{3}{4}) \ (\frac{3}{4},\frac{5}{2})2x+3y=9 \end{gathered}$

Solutions · 1