KCET 2026 | Differential Equations Question 1 | Mathematics

Sum of the squares of the order and degree (if defined) of a differential equation $2 y^{\prime}+\left(y^{\prime \prime}\right)^2=\sqrt{y^{\prime \prime}-3}$ is

$3$

$20$

$8$

$16$

KCET 2026

MCQ (Single Correct Answer)

-0

$\int xf(x)\,dx + \dfrac{f(x)}{2} = 0$, then $f(x)$ is equal to

$e^{-2x}$

$e^{2x}$

$e^{-x^2}$

$e^{x^2}$

KCET 2026

MCQ (Single Correct Answer)

-0

Integrating factor of the differential equation $(1 + x^2)\dfrac{dy}{dx} + xy = 1$ is

$1 + x^2$

$\dfrac{1}{2}\log(1 + x^2)$

$\dfrac{x}{1 + x^2}$

$\sqrt{1 + x^2}$

KCET 2025

MCQ (Single Correct Answer)

-0

General solution of the differential equation $\frac{d y}{d x}+y \tan x=\sec x$ is

$y \sec x=\tan x+c$

$y \tan x=\sec x+c$

$\operatorname{cosec} x=y \tan x+c$

$x \sec x=\tan y+c$

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