Question

A function y = f(x) satisfies the differential equation `(dy)/(dx) + x^2y` = –2x, f(1) = 1. the value of |f"(1)| is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

A function y = f(x) satisfies the differential equation `(dy)/(dx) + x^2y` = –2x, f(1) = 1. the value of |f"(1)| is 1.00.

Explanation:

f'(x) + x²f(x) = –2x, f(1) = 1

⇒ f'(1) + 1 = –2

⇒ f'(1) = –3

f''(x) + 2xf(x) + x²f'(x) = –2

f''(1) + 2f(1) + f'(1) = –2

f''(1) = 3 – 4 = –1

⇒ |f''(1)| = 1