JEE Advance 2025 Paper 1

Given $\frac{dy_1}{dx} - (\sin^2 x)y_1 = 0, y_1(1)=5$  ; $\frac{dy_2}{dx} - (\cos^2 x)y_2 = 0, y_2(1)=1/3$  ; $\frac{dy_3}{dx} - \frac{2-x^3}{x^3} y_3 = 0, y_3(1)=3/(5e)$  . Find $\lim_{x \to 0^+} \frac{y_1(x)y_2(x)y_3(x) + 2x}{e^{3x} \sin x}$  .