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Short Quiz - Chapter 9 Class 12 Differential Equations

Chapter 9 Class 12 Differential Equations | 5 questions

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Question 1 of 5
Question 1 of 5
CBSE Board Exam 2026
Assertion (A) : One of the particular solutions of the differential equation \(\frac{d y}{d x}=e^{x+y}\) can be \(e^{x}+e^{-y}=-2\).
Reason \((R): \quad \mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{y}}=\mathrm{C}\) is the general solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\).
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Question 2 of 5
CBSE Board Exam 2026
\(\frac{d y}{d x}=F(x, y)\) will be a homogeneous differential equation for which of the following functions?
(i) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=3 \mathrm{x}+2 \mathrm{y}\)
(ii) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\sin \frac{\mathrm{y}}{\mathrm{x}}+\log \mathrm{y}-\log \mathrm{x}\)
(iii) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\mathrm{e}^{\mathrm{y} / \mathrm{x}}+1\)
(iv) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}}-\mathrm{y}\)
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Question 3 of 5
CBSE Board Exam 2025
If \(y=\sin ^{-1} x\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}\) is equal to :
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Question 4 of 5
CBSE Board Exam 2025
If \(p\) and \(q\) are respectively the order and degree of the differential equation \(\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{\mathrm{dy}}{\mathrm{d} x}\right)^3=0\), then \((\mathrm{p}-\mathrm{q})\) is
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Question 5 of 5
CBSE Board Exam 2024
\(x \log x \frac{d y}{d x}+y=2 \log x\) is an example of \(a:\)
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