What is the solution for x^2y^{''}-7xy^'+15y=0,y(1)=0,y^'(1)=2 ?

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

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x^2y^{''}-7xy^'+15y=0,y(1)=0,y^'(1)=2

x^{2} y^{^{''}} - 7 x y^{^{'}} + 15 y = 0, y (1) = 0, y^{^{'}} (1) = 2

y = x^{5} - x^{3}

Solution steps

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

Solve linear ODE:

y = x^{5} - x^{3}

y = x^{5} - x^{3}

\frac{d}{d x} (\frac{x}{x ^{4} + 4})

\frac{d}{d x} (\frac{x ^{4}}{5 - x ^{3}})

f (x) = ln (5 + ln (x))

3 t e^{- t}

\int_{2}^{e + 1} \frac{1}{x - 1} d x

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