What is the solution for (dy)/(dx)=(x^2+y^2)/(x^2) ?

The solution for (dy)/(dx)=(x^2+y^2)/(x^2) is y=(sqrt(3)xtan((sqrt(3)(ln(x)+c_{1}))/2))/(2)+1/2 x

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(dy)/(dx)=(x^2+y^2)/(x^2)

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

y = \frac{3 x tan ( \frac{3 ( l n ( x ) + c _{1} )}{2} )}{2} + \frac{1}{2} x

Solution steps

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

Solve using substitution:

y = \frac{3 x tan ( \frac{3 ( l n ( x ) + c _{1} )}{2} )}{2} + \frac{1}{2} x

y = \frac{3 x tan ( \frac{3 ( l n ( x ) + c _{1} )}{2} )}{2} + \frac{1}{2} x

(\frac{x}{x ^{2} + y ^{4}}) d x + (\frac{( 2 y ^{3} )}{x ^{2} + y ^{4}}) d y = 0

\frac{d}{d x} (\frac{7 x ^{3} + x}{6 x})

\frac{d}{d x} (lo g_{10} (\frac{1}{x}))

\int \frac{1}{y ( y ^{3} - 1 )} d y

y^{^{''}} - 6 y^{^{'}} = 4 x

What is the solution for (dy)/(dx)=(x^2+y^2)/(x^2) ?
The solution for (dy)/(dx)=(x^2+y^2)/(x^2) is y=(sqrt(3)xtan((sqrt(3)(ln(x)+c_{1}))/2))/(2)+1/2 x