What is the solution for (dy)/(dx)=(35)/(y^{1/6)+49x^2y^{1/6}} ?

The solution for (dy)/(dx)=(35)/(y^{1/6)+49x^2y^{1/6}} is y=((35arctan(7x)+c_{1})/6)^{6/7}

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(dy)/(dx)=(35)/(y^{1/6)+49x^2y^{1/6}}

\frac{d y}{d x} = \frac{35}{y ^{\frac{1}{6}} + 49 x ^{2} y ^{\frac{1}{6}}}

y = (\frac{35 arctan ( 7 x ) + c _{1}}{6})^{\frac{6}{7}}

Solution steps

\frac{d y}{d x} = \frac{35}{y ^{\frac{1}{6}} + 49 x ^{2} y ^{\frac{1}{6}}}

Solve separable ODE:

y = (\frac{35 arctan ( 7 x ) + c _{1}}{6})^{\frac{6}{7}}

y = (\frac{35 arctan ( 7 x ) + c _{1}}{6})^{\frac{6}{7}}

\frac{d y}{d x} y = - 6 x^{\frac{3}{2}}

\frac{d y}{d x} = (\frac{1 + y ^{2}}{1 + x ^{2}})

\frac{d y}{d x} = \frac{2 y ^{2}}{x}, y (9) = \frac{1}{49}

sin (2 x) d x + cos (3 y) d y = 0, y (\frac{π}{2}) = (\frac{π}{3})

\frac{d P}{d t} = 8 Pt, P (1) = 7

What is the solution for (dy)/(dx)=(35)/(y^{1/6)+49x^2y^{1/6}} ?
The solution for (dy)/(dx)=(35)/(y^{1/6)+49x^2y^{1/6}} is y=((35arctan(7x)+c_{1})/6)^{6/7}