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Differential Equations question

2024 · 27 Jan · Shift 1 · Q36

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JEE Main
Mathematics
Differential Equations
2024 · 27 Jan · Shift 1 · Q36

Differential Equations question

2024 · 27 Jan · Shift 1 · Q36

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

x=x(\mathrm{t})

and

y=y(\mathrm{t})

be solutions of the differential equations

\frac{\mathrm{d} x}{\mathrm{dt}}+\mathrm{a} x=0

and

\frac{\mathrm{d} y}{\mathrm{dt}}+\mathrm{by}=0

respectively,

\mathrm{a}, \mathrm{b} \in \mathbf{R}

. Given that

x(0)=2 ; y(0)=1

and

3 y(1)=2 x(1)

, the value of

\mathrm{t}

, for which

x(\mathrm{t})=y(\mathrm{t})

, is :

A
$\log _{\frac{2}{3}} 2$
B
$\log _{\frac{4}{3}} 2$
C
$\log _4 3$
D
$\log _3 4$

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