Let Y=Y(X) be a curve lying in the first quadrant such that the area enclosed by the tange…

Question

Let $Y=Y(X)$ be a curve lying in the first quadrant such that the area enclosed by the tangent line $Y-y=Y'(x)(X-x)$ and the coordinate axes, where $(x,y)$ is any point on the curve, is always $-\dfrac{y^2}{2Y'(x)}+1$, $Y'(x)
e0$. If $Y(1)=1$, then $12Y(2)$ equals \_\_\_\_\_\_\_\_.

Answer: 20

Accepted Answer

*(This is a differential-equation problem whose full derivation is corrupted in the source. The stated answer is $20$.)*

Solutions · 1