1
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following in respect of the differential equation :

$${{{d^2}y} \over {d{x^2}}} + 2{\left( {{{dy} \over {dx}}} \right)^2} + 9x = x$$

1. The degree of the differential equation is 1.

2. The order of the differential equation is 2.

Which of the above statements is/are correct?
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
2
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is the general solution of the differential equation $${{dy} \over {dx}} + {x \over y} = 0$$ ?
A
$${x^2} + {y^2} = C$$
B
$${x^2} - {y^2} = C$$
C
$${x^2} + {y^2} = Cxy$$
D
$$x + y = C$$
3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let $y_1(x)$ and $y_2(x)$ be two solutions of the differential equation $\frac{dy}{dx} = x$. If $y_1(0) = 0$ and $y_2(0) = 4$, then what is the number of points of intersection of the curves $y_1(x)$ and $y_2(x)$?

A

No point

B

One point

C

Two points

D

More than two points

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

The differential equation, representing the curve $y = e^{x}(a\cos{x} + b\sin{x})$ where $a$ and $b$ are arbitrary constants, is

A

$\frac{d^2y}{dx^2} + 2y = 0$

B

$\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + 2y = 0$

C

$\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 2y = 0$

D

$\frac{d^2y}{dx^2} + y = 0$

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