What is the solution for 2t^2y^{''}+3ty^'-y=0 ?

The solution for 2t^2y^{''}+3ty^'-y=0 is y=c_{1}sqrt(t)+(c_{2})/t

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2t^2y^{''}+3ty^'-y=0

2 t^{2} y^{^{''}} + 3 t y^{^{'}} - y = 0

y = c_{1} t + \frac{c _{2}}{t}

Solution steps

2 t^{2} y^{''} (t) + 3 t y^{'} (t) - y = 0

Solve linear ODE:

y = c_{1} t + \frac{c _{2}}{t}

y = c_{1} t + \frac{c _{2}}{t}

\int_{0}^{\infty} e^{- \frac{x}{2}} d x

\int_{0}^{3} (3 x - x^{2}) d x

3 e^{- 2 t} cos (3 t)

x \to 3 lim (\frac{1}{3 - x})

y^{^{'}} = \frac{4 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

What is the solution for 2t^2y^{''}+3ty^'-y=0 ?
The solution for 2t^2y^{''}+3ty^'-y=0 is y=c_{1}sqrt(t)+(c_{2})/t