What is the solution for x^2(d^2y)/(dx^2)-7x(dy)/(dx)+16y=0 ?

The solution for x^2(d^2y)/(dx^2)-7x(dy)/(dx)+16y=0 is y=c_{1}x^4+c_{2}ln(x)x^4

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x^2(d^2y)/(dx^2)-7x(dy)/(dx)+16y=0

x^{2} \frac{d ^{2} y}{d x ^{2}} - 7 x \frac{d y}{d x} + 16 y = 0

y = c_{1} x^{4} + c_{2} ln (x) x^{4}

Solution steps

x^{2} \frac{d ^{2} y}{d x ^{2}} - 7 x \frac{d y}{d x} + 16 y = 0

Solve linear ODE:

y = c_{1} x^{4} + c_{2} ln (x) x^{4}

y = c_{1} x^{4} + c_{2} ln (x) x^{4}

y^{^{'}} + 0.5 y = 2

\int (2 t - t - \frac{9}{t ^{2}}) d t

x \to - 6 + lim (f (x))

\frac{\partial}{\partial x} (x^{4} + 6 y - 10)

f (x) = \frac{ln ( 8 x )}{e ^{5 x}}

What is the solution for x^2(d^2y)/(dx^2)-7x(dy)/(dx)+16y=0 ?
The solution for x^2(d^2y)/(dx^2)-7x(dy)/(dx)+16y=0 is y=c_{1}x^4+c_{2}ln(x)x^4