Which of the following transformation reduces the differential equation dz - dx - z - x log z - z - x 2log z 2 to the form P x u - Q x A- u -log z -2B- u -log zC- u - e zD- u -log z -1

The correct option is D u = (log z)^ 1Given equ. Can be written as dx/z (In z)^2 + dx/x (In z) = dx/x^2 put u = 1/In z du/dx = 1/(In z)^2. 1/z . dz/dx ∴ d ...

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Byju's Answer

Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

Which of the ...

Question

Which of the following transformation reduces the differential equation $\frac{d z}{d x} + \frac{z}{x} l o g z = \frac{z}{x^{2}} (l o g z)^{2}$ to the form P(x)u = Q(x)

u = l o g z

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u = e^{z}

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u = (l o g z)^{- 1}

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u = (l o g z)^{- 2}

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Solution

The correct option is C $u = (l o g z)^{- 1}$
Given equ. Can be written as
$\frac{d x}{z (I n z)^{2}} + \frac{d x}{x (I n z)} = \frac{d x}{x^{2}} p u t u = \frac{1}{I n z} \frac{d u}{d x} = - \frac{1}{(I n z)^{2}} . \frac{1}{z} . \frac{d z}{d x} ∴ - \frac{d u}{d x} + \frac{1}{x} . u = \frac{1}{x^{2}} \frac{d u}{d x} + (- \frac{1}{x}) u = (- \frac{1}{x^{2}}) I . F . = e^{\int - \frac{1}{x}} = e^{I n \frac{1}{x} =} \frac{1}{x} u . \frac{1}{x} = \int - \frac{1}{x^{2}} . \frac{1}{x} d x \frac{u}{x} = - \int \frac{1}{x^{3}} d x = + \frac{1}{4 x^{4}} + c$

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Similar questions

Q. Which of the following transformations reduce the differential equation

\frac{d z}{d x} + \frac{z}{x} \log z = \frac{z}{x^{2}} {(\log z)}^{2}

into the form

\frac{d u}{d x} + P (x) u = Q (x)

(a) u = log x
(b) u = e^z
(c) u = (log z)⁻¹
(d) u = (log z)²

Q. Which of the following transformation reduce the differential equation

\frac{d z}{d x} + \frac{z}{x} log z = z (log z)^{2} f (x)

into the form

\frac{d u}{d x} + P (x) (u) = Q (x)

Q. Solve the differential equation:

\frac{d z}{d x} + \frac{z}{x} log z = \frac{z}{x^{2}} {(log z)}^{2}

Q. Which of the following transformation reduce the differential equation

\frac{d z}{d x} + \frac{z}{x} log z = \frac{z}{x^{2}} {(log z)}^{2}

into the form

\frac{d v}{d x} + P (x) v = Q (x)

Q. Which of the following transformation reduces the differential equation

\frac{d z}{d x} + \frac{z}{x} l n z = \frac{z}{x^{2}} (l n z)^{2}

into the form

\frac{d u}{d x} + p (x) u = Q (x) ?

Where P(x) and Q(x) are function of x.

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Which of the following transformation reduces the differential equation dzdx+zxlogz=zx2(logz)2 to the form P(x)u = Q(x)

The correct option is C u=(logz)−1Given equ. Can be written as dxz(Inz)2+dxx(Inz)=dxx2put u=1Inzdudx=−1(Inz)2.1z.dzdx∴−dudx+1x.u=1x2dudx+(−1x)u=(−1x2)I.F.=e∫−1x=eIn1x=1xu.1x=∫−1x2.1xdxux=−∫1x3dx=+14x4+c

Which of the following transformation reduces the differential equation $\frac{d z}{d x} + \frac{z}{x} l o g z = \frac{z}{x^{2}} (l o g z)^{2}$ to the form P(x)u = Q(x)