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PREVIOUS
1
IAT (IISER) 2023
MCQ (Single Correct Answer)
+4
-1
Which of the following differential equations has $y=e^x$ as one of its particular solutions?
A
$y \frac{d^2 y}{d x^2}+e^x \frac{d y}{d x}+y^2=e^{2 x}$
B
$y \frac{d^2 y}{d x^2}-e^x \frac{d y}{d x}+y^2=e^{2 x}$
C
$y \frac{d^2 y}{d x^2}-e^x \frac{d y}{d x}+y^2=e^x$
D
$y \frac{d^2 y}{d x^2}+e^x \frac{d y}{d x}+y^2=e^x$
2
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1
For arbitrary constants $\alpha, \beta$, the differential equation representing the family of curves $y=$ $(\alpha x+\beta) e^x$ is
A
$y^{\prime \prime}-2 y^{\prime}+y=0$
B
$y^{\prime \prime}-y^{\prime}+y=0$
C
$y^{\prime \prime}-2 y^{\prime}-y=0$
D
$y^{\prime \prime}-y^{\prime}-y=0$
3
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
Consider the differential equation $f^{\prime \prime}+p f^{\prime}+q f=0$ where $p$ and $q$ are constants, $p^2=4 q$ and $q \neq 0$. If y is a nonzero solution of the equation, then which of the following statements is correct?
A
$(1+x) y$ can never be a solution
B
$y^2$ can never be a solution
C
$y^{\prime}$ can never be a solution
D
$x y$ can never be a solution
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