COMEDK 2026 Morning Shift | Differential Equations Question 8 | Mathematics

$$ \text { The particular solution of the equation } \sin \left(\frac{d y}{d x}\right)=a \text {, where } a \in \mathbb{R} \text { and } y=2 \text { when } x=0 \text { is } $$

$$ \sin \left(\frac{y-2}{x}\right)=a $$

$$ \sin \left(\frac{x-2}{y}\right)=a $$

$$ \sin \left(\frac{y+2}{x}\right)=a $$

$$ \sin \left(\frac{x}{y-2}\right)=a $$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

The solution of the differential equation: $x \cos y d y=\left(x e^x \log x+e^x\right) d x$ is

$\sin y-e^x \log x=c$

$\sin y=e^x \log x+c$

$\sin y=e^x+\log x+c$

$\sin y=\frac{e^x}{x}+c$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$, when $y(1)=2$ is :

two

one

zero

infinite

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

Find the function ' $f$ ' which satisfies the equation $\frac{d f}{d x}=2 f$, given that $f(0)=e^3$

$2 x+3$

$\log (2 x+3)$

$e^{2 x+3}$

$\frac{x^2}{2}$

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