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Angle between Two Planes

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the real value of n for which substitution y=u^n will tranform differential equation 2x^4ydy/dx+y^4=4x^6,into a homogeneous equatio

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Q. The real value of n for which substitution

y = u^{n}

will transform differential equation

2 x^{4} y \frac{d y}{d x} + y^{4} = 4 x^{6}

into homogeneous equation

Q. The real value for

n

for which the substitution

y = u^{n}

will transform the differential equation

2 x^{4} y \frac{d y}{d x} + y^{4} = 4 x^{4}

into a homogeneous equation is

Q. The real value of

m

for which the substitution

y = u^{m}

will transform the differential equation

2 x^{4} \cdot y \frac{d y}{d x} + y^{4} = 4 x^{6}

into a homogeneous equation, is

Q. The substitution

y = z^{α}

transforms the differential equation

(x^{2} y^{2} - 1) d y + 2 x y^{3} d x = 0

into a homogeneous differential equation for

Q. A homogeneous differential equation of the from

\frac{d x}{d y} = h (\frac{x}{y})

can be solved by making the substitution:

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