JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Understanding +4 | -1

The degree and the order of

\left.y=x \frac{d^2 y}{d x^2}+3 \sqrt{1+\left(\frac{d^3 y}{d x^3}\right.}\right)^3

are and respectively.

View answer and explanation

Correct option: B

3,3

Option B (3,3) is correct because after removing the radical, the highest order derivative is 3 and its power is 3.

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y=y(x)

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{x^2} + {y^2} = 1

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x = A\cos 4t + B\sin 4t,

\frac{{{d^2}x}}{{d{t^2}}}

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y=y(t)

\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}

\alpha>0, \beta>0

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\lim \limits_{{x \rightarrow \infty}} y(t)