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

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

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(d^2y)/(dx^2)=((dy)/(dx))^2

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

y = - ln (x + c_{1}) + c_{2}

Solution steps

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

Solve using substitution:

y = - ln (x + c_{1}) + c_{2}

y = - ln (x + c_{1}) + c_{2}

4 y^{^{''}} + 7 y = 0

\frac{\partial}{\partial x} (- 3 y)

\frac{\partial}{\partial x} (e^{2 x} - x cos (t))

5 \frac{d y}{d x} + 30 y = 6

f (x) = \frac{1}{x ^{2}}

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