What is the solution for x^2+2xy+x(dy)/(dx)=0 ?

The solution for x^2+2xy+x(dy)/(dx)=0 is y=-(2x-1)/4+(c_{1})/(e^{2x)}

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x^2+2xy+x(dy)/(dx)=0

x^{2} + 2 x y + x \frac{d y}{d x} = 0

y = - \frac{2 x - 1}{4} + \frac{c _{1}}{e ^{2 x}}

Solution steps

x^{2} + 2 x y + x \frac{d y}{d x} = 0

Solve linear ODE:

y = - \frac{2 x - 1}{4} + \frac{c _{1}}{e ^{2 x}}

y = - \frac{2 x - 1}{4} + \frac{c _{1}}{e ^{2 x}}

d er i v a t i v e 3 x^{4} - 65 x^{3}

\int 2 sec^{4} (x) d x

\int - \frac{5000}{x ^{2}} d x

\frac{d}{d x} (2^{x} + 3^{x})

\frac{d}{d x} (\frac{3 x ^{2} + 5 x}{x})

What is the solution for x^2+2xy+x(dy)/(dx)=0 ?
The solution for x^2+2xy+x(dy)/(dx)=0 is y=-(2x-1)/4+(c_{1})/(e^{2x)}