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Differential Equations Maths - Differential Equations

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 44 questions in this chapter.

Question types

Differential Equations question types

44 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

44
Questions
6
Question groups
5
Question types
Sample Questions

Differential Equations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q (1 Marks)1 Mark
The degree of the differential equation $x y \frac{d^2 y}{d x^2}+x\left(\frac{d y}{d x}\right)^3-y \frac{d y}{d x}=0$ is :
  • A
    3
  • ✓
    1
  • C
    $0$
  • D
    2

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark
The degree of differential equation $\sqrt{1+\left(\frac{d y}{d x}\right)^2}=$ $a\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}:$
  • A
    1
  • ✓
    2
  • C
    3
  • D
    4

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark
The solution of the equation $\frac{d y}{d x}=\frac{1-\cos 2 y}{1+\cos 2 y}$ is :
  • A
    $x+\tan y+y=c$
  • B
    $x+\cot y-y=c$
  • C
    $x+\tan y-y=c$
  • ✓
    $x+\cot y+y=c$

Answer: D.

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Q 175 Marks Questions5 Marks
Find a particular solution of the differential equation $\frac{ dy }{ dx }+2 y \cot x=4 x \operatorname{cosec} x$ $(x \neq 0)$, given that $y=0$, when $x=\frac{\pi}{2}$.
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Q 185 Marks Questions5 Marks
Find a particular solution of the differential equation $\left(1+ x ^2\right) d y+2 \ x y \ d x=\cot x d x$, given that $y=0$ of $x=\frac{\pi}{2}$.
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