Differential Equations - Maharashtra Board STD 12 Science Maths Questions

Q 1MCQ2 Marks

The order and degree of the differential equation $\frac{d^2 y}{d x^2}+\frac{d y}{d x}+x=\sqrt{1+\frac{d^3 y}{d x^3}}$ are respectively____.

A
2,3
B
3,2
C
1,3
D
3,1

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Q 2MCQ2 Marks

The solution of the differential equation $\frac{d y}{d x}=\sec x-y \tan x$ is .....

✓
$y \sec x=\tan x+ c$
B
$y \sec x+\tan x=c$
C
$\sec x=y \tan x+c$
D
$\sec x+y \tan x=c$

Answer: A.

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Q 3MCQ2 Marks

The differential equation of the family of curves $y=c_1 e^x+c_2 e^{-x}$ is .....

A
$\frac{d^2 y}{d x^2}+y=0$
B
$\frac{d^2 y}{d x^2}-y=0$
C
$\frac{d^2 y}{d x^2}+1=0$
D
$\frac{d^2 y}{d x^2}-1=0$

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Q 4MCQ2 Marks

Order and degree of differential equation $\frac{d^4 y}{d x^4}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^3$ respectively are ______.

A
Order : 1, Degree : 4
B
Order : 4, Degree : 1
C
Order : 6, Degree : 1
D
Order : 1, Degree : 6

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Q 5MCQ2 Marks

If $y=a e^{5 x}+b e^{-6 x}$, then the differential equation is $\qquad$

A
$\frac{d^2 y}{d x^2}=25 y$
B
$\frac{d^2 y}{d x^2}=-25 y$
C
$\frac{d^2 y}{d x^2}=-5 y$
D
$\frac{d^2 y}{d x^2}=5 y$

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Q 6Answer the following questions in short.1 Mark

Write the degree of the differental equation
$
\left(y^{\prime \prime \prime}\right)^2+3\left(y^{\prime \prime}\right)+3 x y^{\prime}+5 y=0
$

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Q 7Solve the Following Question.(2 Marks)2 Marks

Solve the differential equation $\sec ^2 x \cdot \tan y d x+\sec ^2 y \cdot \tan x \cdot d y=0$

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Q 8Solve the Following Question.(2 Marks)2 Marks

Solve the differential equation : $y-x \frac{d y}{d x}=0$

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Q 9Solve the Following Question.(2 Marks)2 Marks

Form the differentilal equation of all lines which makes intercept 3 on $x$-axis.

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Q 10Solve the Following Question.(2 Marks)2 Marks

Solve the differential equation $y \frac{d y}{d x}+x=0$

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Q 11Solve the Following Question.(2 Marks)2 Marks

Solve the differential equation $\frac{d y}{d x}=x^2 y+y$

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Q 12Solve the Following Question.(3 Marks)3 Marks

Solve: $3 e^x \tan y d x+\left(1+e^x\right) \sec ^2 y d y=0$. Also, find the particular solution when $x=0$ and $y=\pi$.

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Q 13Solve the Following Question.(3 Marks)3 Marks

Solve: $x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$

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Q 14Solve the Following Question.(3 Marks)3 Marks

Solve the differential equation $\frac{d y}{d x}+y=e^{-x}$

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Q 15Solve the Following Question.(3 Marks)3 Marks

If the population of a country doubles in 60 years, in how many years will it be triple under the assumption that the rate of increase in proportional to the number of inhabitants? [Given : $\log 2=0.6912$ and $\log 3=1.0986$ ]

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Q 16Solve the Following Question.(3 Marks)3 Marks

Solve. $\frac{d y}{d x}=\cos (x+y)$

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Q 17Solve the Following Question.(4 Marks)4 Marks

Solve the differential equation $\left(x^2+y^2\right) d x-2 x y d y=0$

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Q 18Solve the Following Question.(4 Marks)4 Marks

Solve the differential equation : $x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$. Also find the particular solution if $x=y=0$

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Q 19Solve the Following Question.(4 Marks)4 Marks

Solve the differential equation : $\cos ^2 x \frac{d y}{d x}+y=\tan x$

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Q 20Solve the Following Question.(4 Marks)4 Marks

Solve the differential equation : $(x+y) \frac{d y}{d x}=1$.

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Q 21Solve the Following Question.(4 Marks)4 Marks

Solve the differential equation : $\frac{d y}{d x}+y \sec x=\tan x$.

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Differential Equations question types

Differential Equations questions

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Differential Equations Maths - Differential Equations

Differential Equations question types

Differential Equations questions

Generate a Differential Equations paper free