If the solution of the differential equation dy/dx + eˣ(x² - 2)y = (x² - 2x)(x² - 2)e²ˣ satisfies y(0) = 0, then the value of y(2) is _ _ _ _ _ _ _ _.

Differential Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jun, Evening shift · Q3543

JEE Main 202226 Jun, Evening shiftMathematicsMediumDifferential Equations163× since 2002

If the solution of the differential equation

{{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x} \right)\left( {{x^2} - 2} \right){e^{2x}}

satisfies

y(0) = 0

, then the value of y(2) is _______________.

JEE Main 2022 · 26 Jun, Evening shift · Q3543

JEE Main 202226 Jun, Evening shiftMathematicsMediumDifferential Equations163× since 2002

If the solution of the differential equation

{{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x} \right)\left( {{x^2} - 2} \right){e^{2x}}

satisfies

y(0) = 0

, then the value of y(2) is _______________.