What is the solution for (d^2y)/(dx^2)= 1/x+2 ?

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

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(d^2y)/(dx^2)= 1/x+2

\frac{d ^{2} y}{d x ^{2}} = \frac{1}{x} + 2

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} = \frac{1}{x} + 2

Substitute

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

with

y^{''} (x)

y^{^{''}} (x) = \frac{1}{x} + 2

Solve

y^{''} (x) = \frac{1}{x} + 2 : y^{'} (x) = ln (x) + 2 x + c_{1}

Solve

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

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

x \to - 2 lim (\frac{∣ x - 2 ∣}{x - 2})

\frac{\partial}{\partial x} ((x^{3} + y^{3})^{10})

\int \frac{5 - x ^{2}}{3 x ^{3} + x} d x

f (x) = x e^{3 x}

\frac{\partial}{\partial x} (tan (6 + 2 x^{2} y^{4} z^{2}))

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