What is the solution for (dy)/(dx)=(y^2+xy+x^2)/(x^2),y(1)=-1 ?

The solution for (dy)/(dx)=(y^2+xy+x^2)/(x^2),y(1)=-1 is y=tan(ln(x)+(3pi)/4+pin)x

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(dy)/(dx)=(y^2+xy+x^2)/(x^2),y(1)=-1

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

y = tan (ln (x) + \frac{3 π}{4} + πn) x

Solution steps

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

Solve using substitution:

y = tan (ln (x) + \frac{3 π}{4} + πn) x

y = tan (ln (x) + \frac{3 π}{4} + πn) x

What is the solution for (dy)/(dx)=(y^2+xy+x^2)/(x^2),y(1)=-1 ?
The solution for (dy)/(dx)=(y^2+xy+x^2)/(x^2),y(1)=-1 is y=tan(ln(x)+(3pi)/4+pin)x