A curve satisfying the initial condition, y(1)=0, satisfies the differential equation, x (d y/d x)=y-x2. The area bounded by the curve and the x-axis is

Question

A curve satisfying the initial condition, y(1)=0, satisfies the differential equation, x (d y/d x)=y-x2. The area bounded by the curve and the x-axis is (A) (1/2) (B) (1/3) (C) (1/4) (D) (1/6)

Tardigrade Admin · Accepted Answer

equation of the curve is y = x (1 - x)

Q. A curve satisfying the initial condition, $y (1) = 0$ , satisfies the differential equation, $x \frac{d y}{d x} = y - x^{2}$ . The area bounded by the curve and the $x$ -axis is

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{6}$

equation of the curve is $y = x (1 - x)$

Q. A curve satisfying the initial condition, y(1)=0, satisfies the differential equation, xdxdy​=y−x2. The area bounded by the curve and the x-axis is

21​

31​

41​

61​