ISRO 2012- [Mech] Calculus

Question

The approximate value of y(0.1) from dy/dx = $x^2$y-1, y(0) =1 is

(a) 0.900

(b) 1.001

(c) 0.802

(d) 0.994

Answer 1

By solving using Euler's method. $x_0 = 0, y_0 = 1, x_1 = 0.1$

At $(x_0, y_0)$, $\frac{dy}{dx} = x^2y - 1 = -1$.

Now, $\frac{dy}{dx} \approx \frac{y_1 - y_0}{x_1 - x_0}$.

On putting values, you get $y_1 = 0.9$.

Hence, D = $0.9$ is the answer.

Comments

May you please give ref link to know about Euler's method.