JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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To reduce the differential equation

\frac{{dy}}{{dx}} + P\left( x \right).y = Q\left( x \right).{y^n}

to the linear form, the substitution is

View answer and explanation

Correct option: B

v = \frac{1}{{{y^{n - 1}}}}

Option B (

v = \frac{{1}}{{{y^{n - 1}}}}}}

) is correct because this substitution transforms the Bernoulli equation into a linear differential equation.

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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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x

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

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

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y=y(t)

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

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