What is the solution for y^{''}-5y^'=0,y(0)=6,y^'(0)=-9 ?

The solution for y^{''}-5y^'=0,y(0)=6,y^'(0)=-9 is y=(6-39/5)e^{5t}+39/5

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y^{''}-5y^'=0,y(0)=6,y^'(0)=-9

y^{^{''}} - 5 y^{^{'}} = 0, y (0) = 6, y^{^{'}} (0) = - 9

y = (6 - \frac{39}{5}) e^{5 t} + \frac{39}{5}

Solution steps

y^{''} (t) - 5 y^{'} (t) = 0

Solve linear ODE:

y = (6 - \frac{39}{5}) e^{5 t} + \frac{39}{5}

y = (6 - \frac{39}{5}) e^{5 t} + \frac{39}{5}

\frac{\partial}{\partial x} (ln (x^{4} - y^{4}))

\frac{d}{d x} (I n^{4} x)

\frac{5 x + 1}{5 x - 1}

y = x, y = x^{6}

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

What is the solution for y^{''}-5y^'=0,y(0)=6,y^'(0)=-9 ?
The solution for y^{''}-5y^'=0,y(0)=6,y^'(0)=-9 is y=(6-39/5)e^{5t}+39/5