What is the solution for y^{''}-5y+6y=0,y(0)=-3/5 ,y^'(0)=-13/5 ?

The solution for y^{''}-5y+6y=0,y(0)=-3/5 ,y^'(0)=-13/5 is y=-3/5 cos(t)-13/5 sin(t)

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y^{''}-5y+6y=0,y(0)=-3/5 ,y^'(0)=-13/5

y^{^{''}} - 5 y + 6 y = 0, y (0) = - \frac{3}{5}, y^{^{'}} (0) = - \frac{13}{5}

y = - \frac{3}{5} cos (t) - \frac{13}{5} sin (t)

Solution steps

y^{''} (t) - 5 y + 6 y = 0

Solve linear ODE:

y = - \frac{3}{5} cos (t) - \frac{13}{5} sin (t)

y = - \frac{3}{5} cos (t) - \frac{13}{5} sin (t)

5 y^{^{''}} + 9 y^{^{'}} = 0

y^{^{''}} + 14 y^{^{'}} = 0, y (0) = - 7

y^{^{''''}} = 81 y

y^{^{''}} + 16 y^{^{'}} + 8 y = 0

y^{^{''}} + y^{^{'}} - 2 y = 0, y^{0} = 1, y^{^{'}} 0 = 1

What is the solution for y^{''}-5y+6y=0,y(0)=-3/5 ,y^'(0)=-13/5 ?
The solution for y^{''}-5y+6y=0,y(0)=-3/5 ,y^'(0)=-13/5 is y=-3/5 cos(t)-13/5 sin(t)