Differential Equations · Mathematics · COMEDK

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MCQ (Single Correct Answer)

1
The solution of the differential equation: $x \cos y d y=\left(x e^x \log x+e^x\right) d x$ is
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2
The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$, when $y(1)=2$ is :
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3
Find the function ' $f$ ' which satisfies the equation $\frac{d f}{d x}=2 f$, given that $f(0)=e^3$
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4
Solve the following differential equation $\cos ^2 x \frac{d y}{d x}+y=\tan x$, given that $y(0)=1$. Hence find $y\left(\frac{\pi}{4}\right)$
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5
Integrating factor of the differential equation $\frac{d y}{d x}+y=\frac{x^3+y}{x}$ is
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6
The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{4}}=\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}$
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7
Which of the following transformations reduce the differential equation $\frac{d z}{d x}+\frac{z}{x} \log z=\frac{z}{x^2}(\log z)^2$ into the form $\frac{d u}{d x}+P(x) u=Q(x)$
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8
Solution of the differential equation $y \frac{d y}{d x}+x=0$ represents a family of
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9
The solution of $(x+\log y) d y+y d x=0$ when $y(0)=1$ is
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10
The order of the differential equation $\frac{d}{d x}\left[\left(\frac{d y}{d x}\right)^3\right]=0$ is
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11
The general solution of the differential equation $(x-y) d y=(x+y) d x$ is
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12
The solution of the differential equation $\frac{d y}{d x}+y \log y \cot x=0$ is
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13

The general solution of the differential equation $$x \frac{d y}{d x}=y+x \tan \left(\frac{y}{x}\right)$$ is

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14

$$ \text { The general solution of the differential equation }(1+\tan y)(d x-d y)+2 x d y=0 \text { is } $$

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15

The sum of the order and degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+\frac{4\left(\frac{d^2 y}{d x^2}\right)^3}{\left(\frac{d^3 y}{d x^3}\right)}+\frac{d^3 y}{d x^3}=x^2-1$$ is

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16

$$ \text { If } \frac{d y}{d x}=y+3>0 \text { and } y(0)=2 \text { then } y(\log 2) \text { is equal to } $$

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17

$$ \text { The general solution of the differential equation } \frac{d y}{d x}=\frac{x y}{x^2+y^2} \text { is } $$

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18

$$ \text { Integrating factor of the differential equation } \frac{d y}{d x}+y=\frac{x^3+y}{x} \text { is } $$

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19

$$ \text { The general solution of } \frac{d y}{d x}=\sin ^{-1} x \text { is } $$

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20

Degree of the differential equation $$\log \left(\frac{d y}{d x}\right)^{\frac{1}{2}}=5 x+4 y$$ is

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21

The particular solution of $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$, when $$x=0, y=\frac{1}{2}$$ is

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22

The particular solution of the differential equation $$\cos x \frac{d y}{d x}+y=\sin x$$ at $$y(0)=1$$

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23

The differential equation of all non-vertical lines in a plane is

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24

The general solution of $$\left(\frac{d y}{d x}\right)^2=1-x^2-y^2+x^2 y^2$$ is

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25

The solution of the differential equation $$\left(\frac{d y}{d x}\right) \tan y=\sin (x+y)+\sin (x-y)$$ is

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26

The particular solution of $$e^{\frac{d y}{d x}}=2 x+1$$ given that $$y=1$$ when $$x=0$$ is

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27

The general solution of the differential equation $$\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$$

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28

The solution of the differential equation $$\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x$$

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29

The sum of the degree and order of the following differential equation $$\left[1-\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=k x \frac{d^2 y}{d x^2}$$

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30

The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ represents

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31

The solution of the differential equation $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$ is

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32

The solution of the differential equation $$x \frac{d y}{d x}=\cot y$$ is

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33

The solution of the differential equation $${\sec ^2}x\tan ydx + {\sec ^2}y\tan xdy = 0$$ is

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34

The solution of the differential equation $$y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\phi '\left( {{{{y^2}} \over {{x^2}}}} \right)}}} \right]$$ is (where, C is a constant)

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35

The solution of the differential equation $$(1 + {y^2}) + (x - {e^{{{\tan }^{ - 1}}y}}){{dy} \over {dx}} = 0$$ is

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36

The differential equation of the family of straight lines whose slope is equal to y-intercept is

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37

The order and degree of the differential equation $${\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^5}} \right]^{{1 \over 3}}} = {{{d^2}y} \over {d{x^2}}}$$ are respectively

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