Question

Solution of the equation x³$\frac{dy}{dx}$ + 4x² tan y = e^x sec y when y(1) = 0 is

• A. sin y = e^x (x –1)x^–4
• B. sin y = e^x (x –1)x^–3
• C. tan y = e^x (x –1)x^–3
• D. tan y = e^x (x –2)log x

Answer 1

Answer: (A)

sin y = e^x (x –1)x^–4

Answer 2

Given equation is x⁴ cosy×$\frac{dy}{dx}$ + 4x³ sin y = x.e^x

$\frac{d}{dx}$ (x⁴ siny) = x×e^x x⁴×sin y = ∫ x×e^x dx

x⁴ siny = (x – 1) e^x + C

in y (1) = 0, x = 1, y = 0 so C = 0

So sol. is siny = x^–4 (x – 1) e^x