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Differential Equations question

2022 · 26 Jun · Shift 2 · Q32

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JEE Main
Mathematics
Differential Equations
2022 · 26 Jun · Shift 2 · Q32

Differential Equations question

2022 · 26 Jun · Shift 2 · Q32

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If

y = y(x)

is the solution of the differential equation

x{{dy} \over {dx}} + 2y = x\,{e^x}

,

y(1) = 0

then the local maximum value of the function

z(x) = {x^2}y(x) - {e^x},\,x \in R

is :

A
1 $-$ e
B
0
C
${1 \over 2}$
D
${4 \over e} - e$

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