Differential Equations jee mains questions | JEE Main Maths Differential Equations Previous Year Question

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Topic Question Set

Q 91 :

Let the solution curve of the differential equation $x d y - y d x = \sqrt{x^{2} + y^{2}} d x, x > 0,$ $y (1) = 0$ be $y = y (x)$ . Then $y (3)$ is equal to [2026]

1
2
6
4

1

2

3

4

(4)

Q 92 :

Let y = y(x) be the solution of the differential equation $\sec x \frac{d y}{d x} - 2 y = 2 + 3 \sin x, x \in (- \frac{π}{2}, \frac{π}{2}),$ $y (0) = - \frac{7}{4} .$ Then $y (\frac{π}{6})$ is equal to: [2026]

$- \frac{5}{2}$
$- \frac{5}{4}$
$- 3 \sqrt{3} - 7$
$- 3 \sqrt{2} - 7$

1

2

3

4

(2)

Q 93 :

Let $f (x) = x^{3} + x^{2} f' (1) + 2 x f'' (2) + f''' (3), x \in ℝ .$ Then the value of f'(5) is [2026]

$\frac{117}{5}$
$\frac{2}{5}$
$\frac{62}{5}$
$\frac{657}{5}$

1

2

3

4

(1)

Q 94 :

If y = y(x) satisfies the differential equation $16 (\sqrt{x + 9 \sqrt{x}}) (4 + \sqrt{9 + \sqrt{x}}) \cos y d y = (1 + 2 \sin y) d x, x > 0$ and $y (256) = \frac{π}{2}, y (49) = α$ , then $2 \sin α$ is equal to_____. [2026]

$3 (\sqrt{2} - 1)$
$\sqrt{2} - 1$
$2 (\sqrt{2} - 1)$
$2 \sqrt{2} - 1$

1

2

3

4

(4)

Q 95 :

Let y = y(x) be the solution of the differential equation $x \frac{d y}{d x} - \sin 2 y = x^{3} (2 - x^{3}) \cos^{2} y, x \neq 0 .$ If y(2) = 0, then $\tan (y (1))$ is equal to... [2026]

$\frac{3}{4}$
$- \frac{3}{4}$
$\frac{7}{4}$
$- \frac{7}{4}$

1

2

3

4

(3)

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