JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

f

be a differentiable function such that

x^2 f(x)-x=4 \int\limits_{0}^x t f(t) d t, f(1)=\frac{2}{3}

. Then

18 f(3)

is equal to

View answer and explanation

Correct option: B

160

Option B (160) is correct because after solving the differential equation and applying the initial condition, we find f(3) and then calculate 18f(3).

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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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\frac{d y}{d x}=y+7

y_{1}(0)=0

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y=y_{1}(x)

y=y_{2}(x)

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)