If y = y(x) is the solution of the equation e^(sin y) cos ydy/dx + e^(sin y) cos x = cos x, y(0) = 0; then 1 + y((π)/6) + (3)/2y((π)/3) + 1/(2)y((π)/4) is equal to _ _ _ _ _ _.

Differential Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 26 Feb, Morning shift · Q35

JEE Main 202126 Feb, Morning shiftMathematicsMediumDifferential Equations163× since 2002

If y = y(x) is the solution of the equation

{e^{\sin y}}\cos y{{dy} \over {dx}} + {e^{\sin y}}\cos x = \cos x

, y(0) = 0; then

1 + y\left( {{\pi \over 6}} \right) + {{\sqrt 3 } \over 2}y\left( {{\pi \over 3}} \right) + {1 \over {\sqrt 2 }}y\left( {{\pi \over 4}} \right)

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 · 26 Feb, Morning shift · Q35

JEE Main 202126 Feb, Morning shiftMathematicsMediumDifferential Equations163× since 2002

If y = y(x) is the solution of the equation

{e^{\sin y}}\cos y{{dy} \over {dx}} + {e^{\sin y}}\cos x = \cos x

, y(0) = 0; then

1 + y\left( {{\pi \over 6}} \right) + {{\sqrt 3 } \over 2}y\left( {{\pi \over 3}} \right) + {1 \over {\sqrt 2 }}y\left( {{\pi \over 4}} \right)

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.