JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Understanding +4 | -1

The order and the degree of

\sqrt[3]{\frac{d^2 y}{d x^2}}=\sqrt{\frac{d y}{d x}}

are and respectively .

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Correct option: D

2,2

Option D (2,2) is correct because after eliminating the fractional powers, the order and degree are both 2.

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y=y(x)

\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0

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\left|(y(2))^{3}-12 y(2)\right|

x

{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_{1}(0)=0

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y=y(t)

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

\alpha>0, \beta>0

\gamma>0

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