What is the solution for 3y^{''}-16y^'+5y=0,y(0)=-3,y^'(0)=4 ?

The solution for 3y^{''}-16y^'+5y=0,y(0)=-3,y^'(0)=4 is y=(-3+57/14)e^{5t}-57/14 e^{t/3}

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3y^{''}-16y^'+5y=0,y(0)=-3,y^'(0)=4

3 y^{^{''}} - 16 y^{^{'}} + 5 y = 0, y (0) = - 3, y^{^{'}} (0) = 4

y = (- 3 + \frac{57}{14}) e^{5 t} - \frac{57}{14} e^{\frac{t}{3}}

Solution steps

3 y^{''} (t) - 16 y^{'} (t) + 5 y = 0

Solve linear ODE:

y = (- 3 + \frac{57}{14}) e^{5 t} - \frac{57}{14} e^{\frac{t}{3}}

y = (- 3 + \frac{57}{14}) e^{5 t} - \frac{57}{14} e^{\frac{t}{3}}

\frac{1}{( x - 4 ) ^{2}}

f (x) = (3 x^{2} + 6 x)^{3}

\int 0.06 x^{2} - 4.4 x + 60 d x

x \to 0 lim (2 x tan (3 x))

f (x) = x^{3} - 2 x^{2} - 3 x

What is the solution for 3y^{''}-16y^'+5y=0,y(0)=-3,y^'(0)=4 ?
The solution for 3y^{''}-16y^'+5y=0,y(0)=-3,y^'(0)=4 is y=(-3+57/14)e^{5t}-57/14 e^{t/3}