What is the solution for (a^3y)/(ax^3)-21(dy)/(dx)-20y=0 ?

The solution for (a^3y)/(ax^3)-21(dy)/(dx)-20y=0 is y=e^{-(20x)/(21)-(a^2)/(42x^2)-c_{1}}

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(a^3y)/(ax^3)-21(dy)/(dx)-20y=0

\frac{a ^{3} y}{a x ^{3}} - 21 \frac{d y}{d x} - 20 y = 0

y = e^{- \frac{20 x}{21} - \frac{a ^{2}}{42 x ^{2}} - c_{1}}

Solution steps

\frac{a ^{3} y}{a x ^{3}} - 21 \frac{d y}{d x} - 20 y = 0

Solve separable ODE:

y = e^{- \frac{20 x}{21} - \frac{a ^{2}}{42 x ^{2}} - c_{1}}

y = e^{- \frac{20 x}{21} - \frac{a ^{2}}{42 x ^{2}} - c_{1}}

y^{^{'}} = x y - 2 x

\frac{d y}{d x} = (2) x

y y^{^{'}} = x - y x, y (1) = 0

y^{^{'}} = y ln (y)

y^{^{'}} = \frac{( 2 - e ^{x} )}{( 3 + 2 y )}

What is the solution for (a^3y)/(ax^3)-21(dy)/(dx)-20y=0 ?
The solution for (a^3y)/(ax^3)-21(dy)/(dx)-20y=0 is y=e^{-(20x)/(21)-(a^2)/(42x^2)-c_{1}}