Let x=x(t) and y=y(t) be solutions of the differential equations (d x)/dt+ ax =0 and dy/dt+ by =0 respectively, a, b ∈ R. Given that x(0)=2; y(0)=1…

Let $\displaystyle x=x(t)$ and $\displaystyle y=y(t)$ be solutions of the differential equations $\displaystyle \frac{\mathrm{d} x}{\mathrm{dt}}+\mathrm{ax}=0$ and $\displaystyle \frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm{by}=0$ respectively, $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbf{R}$. Given that $\displaystyle x(0)=2 ; y(0)=1$ and $\displaystyle 3 y(1)=2 x(1)$, the value of t , for which $\displaystyle x(t)=y(t)$, is :