If y=y(x) is the solution of the differential equation (d y)/(d x)+(4 x)/((x²-1)) y=(x+2)/((x²-1)^(5/2)), x > 1 such that y(2)=2/9 log e (2+√(3)) and y(√(2))=α log e (√(α)+β)+β-√(γ), α, β, γ N, then α β γ is equal to:

Differential Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 13 Apr, Evening shift · Q34

JEE Main 202313 Apr, Evening shiftMathematicsHardDifferential Equations163× since 2002

y=y(x)

is the solution of the differential equation

\frac{d y}{d x}+\frac{4 x}{\left(x^{2}-1\right)} y=\frac{x+2}{\left(x^{2}-1\right)^{\frac{5}{2}}}, x > 1

such that

y(2)=\frac{2}{9} \log _{e}(2+\sqrt{3}) \text { and } y(\sqrt{2})=\alpha \log _{e}(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}, \alpha, \beta, \gamma \in \mathbb{N} \text {, then } \alpha \beta \gamma \text { is equal to }

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2023 · 13 Apr, Evening shift · Q34

JEE Main 202313 Apr, Evening shiftMathematicsHardDifferential Equations163× since 2002

y=y(x)

is the solution of the differential equation

\frac{d y}{d x}+\frac{4 x}{\left(x^{2}-1\right)} y=\frac{x+2}{\left(x^{2}-1\right)^{\frac{5}{2}}}, x > 1

such that

y(2)=\frac{2}{9} \log _{e}(2+\sqrt{3}) \text { and } y(\sqrt{2})=\alpha \log _{e}(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}, \alpha, \beta, \gamma \in \mathbb{N} \text {, then } \alpha \beta \gamma \text { is equal to }

Your answerType your answer. Integers and decimals are accepted.