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

The solution for (dy)/(dx)=(ln(x))/(xy),y(1)=2 is y=sqrt(ln^2(x)+4)

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(dy)/(dx)=(ln(x))/(xy),y(1)=2

\frac{d y}{d x} = \frac{ln ( x )}{x y}, y (1) = 2

y = ln^{2} (x) + 4

Solution steps

\frac{d y}{d x} = \frac{ln ( x )}{x y}

Solve separable ODE:

y = ln^{2} (x) + 4

y = ln^{2} (x) + 4

y = \frac{( t ^{3} + t )}{( t ^{4} - 2 )}

\int \frac{1}{( y ^{2} - 1 )} d y

cos^{3} (x) + sin^{4} (x)

\int \frac{3 x - 2}{x + 1} d x

\frac{\partial}{\partial x} (\frac{2 x ^{2}}{( 2 x + 7 y ) ^{2}})

What is the solution for (dy)/(dx)=(ln(x))/(xy),y(1)=2 ?
The solution for (dy)/(dx)=(ln(x))/(xy),y(1)=2 is y=sqrt(ln^2(x)+4)