1. Tardigrade
  2. Question
  3. Mathematics
  4. Let y=f(x), x ∈ R satisfies the differential equation x(y prime prime+y prime)=-y prime-e-x and y(0)=-1 where y prime=( dy / dx ) and y prime prime=( d 2 y / dx 2). The value of ∫01 ex(f(x)+3) d x is equal to

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Q. Let $y=f(x), x \in R$ satisfies the differential equation $x\left(y^{\prime \prime}+y^{\prime}\right)=-y^{\prime}-e^{-x}$ and $y(0)=-1$ where $y ^{\prime}=\frac{ dy }{ dx }$ and $y ^{\prime \prime}=\frac{ d ^2 y }{ dx ^2}$.
The value of $\int_0^1 e^x(f(x)+3) d x$ is equal to

Application of Integrals

Solution:

Correct answer is (a) e