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

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

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x(d^2y)/(dx^2)+(2(dy)/(dx))=0

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

y = c_{1} + \frac{c _{2}}{x}

Solution steps

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

Solve linear ODE:

y = c_{1} + \frac{c _{2}}{x}

y = c_{1} + \frac{c _{2}}{x}

y^{^{'}} - \frac{4}{x} y = \frac{y ^{3}}{x ^{3}}

\int_{1}^{2} x^{4} (ln (x))^{2} d x

\frac{d}{d x} (- \frac{1}{4 ( x + 1 ) ^{\frac{3}{2}}})

\int_{1}^{2} (\frac{3}{x}) d x

\frac{d}{d x} (\frac{- 5}{x})

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