Question

Let the solution curve of the differential equation $x\frac{dy}{dx}-y=\sqrt{y^2+16x^2},$ y(1) = 3 be y = y(x). Then y(2) is equal to

• A. 15
• B. 11
• C. 13
• D. 17

Answer 1

Answer: (A)

15

Answer 2

The correct option is(A): 15

$x\frac{dy}{dx}-y=\sqrt{y^2+16x^2}$

y = 4 x tan θ

log |secθ + tanθ| = log |x | + C

y(1) = 3 ⇒ 3 = 4 tanθ

⇒ C = ln 2

∴ |secθ + tanθ| = 2|x |

To find y(2) put x = 2

⇒tan⁡θ= $\frac{y}{8}$

(secθ + tanθ)2 = 16

⇒ y = 15