If y = (x + √(1 + x²))ⁿ, then (1 + x²) d²y d x² + xdy/dx is

Limit, Continuity and Differentiability: JEE Main 2002 Mathematics question

JEE Main 2002 · Annual, Paper 1 · Q3662

JEE Main 2002Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

y = {\left( {x + \sqrt {1 + {x^2}} } \right)^n},

then

\left( {1 + {x^2}} \right){{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}}

JEE Main 2002 · Annual, Paper 1 · Q3662

JEE Main 2002Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

y = {\left( {x + \sqrt {1 + {x^2}} } \right)^n},

then

\left( {1 + {x^2}} \right){{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}}