What is the solution for x^2y^{''}-7xy^'+15y=0 ?

The solution for x^2y^{''}-7xy^'+15y=0 is y=c_{1}x^5+c_{2}x^3

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x^2y^{''}-7xy^'+15y=0

x^{2} y^{^{''}} - 7 x y^{^{'}} + 15 y = 0

y = c_{1} x^{5} + c_{2} x^{3}

Solution steps

x^{2} y^{''} (x) - 7 x y^{'} (x) + 15 y = 0

Solve linear ODE:

y = c_{1} x^{5} + c_{2} x^{3}

y = c_{1} x^{5} + c_{2} x^{3}

\int 10 x e^{0.1 x^{2}} d x

\frac{d ^{2} y}{d x ^{2}} = - 25 y

\frac{e ^{2 t} - e ^{1}}{2}

\int_{0}^{1} π (x)^{2} d x

h \to 0 lim (3 h - 1)

What is the solution for x^2y^{''}-7xy^'+15y=0 ?
The solution for x^2y^{''}-7xy^'+15y=0 is y=c_{1}x^5+c_{2}x^3