What is the solution for (d^2y)/(dt^2)-5(dy)/(dt)+6y=0,y(1)=3 ?

The solution for (d^2y)/(dt^2)-5(dy)/(dt)+6y=0,y(1)=3 is y=e^{3t-3}(3-e^2c_{2})+c_{2}e^{2t}

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(d^2y)/(dt^2)-5(dy)/(dt)+6y=0,y(1)=3

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 y = 0, y (1) = 3

y = e^{3 t - 3} (3 - e^{2} c_{2}) + c_{2} e^{2 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 y = 0

Solve linear ODE:

y = e^{3 t - 3} (3 - e^{2} c_{2}) + c_{2} e^{2 t}

y = e^{3 t - 3} (3 - e^{2} c_{2}) + c_{2} e^{2 t}

x^{^{''}} - 3 x^{^{'}} = 0

y^{^{''}} + 36 y = 0, y (0) = 5, y^{^{'}} (0) = - 12

y^{^{''}} + 4 \cdot y^{^{'}} + 4 \cdot y = 0

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = - 1, y^{^{'}} (0) = 9

x^{^{''}} + 3 x^{^{'}} + 3 x = 0

What is the solution for (d^2y)/(dt^2)-5(dy)/(dt)+6y=0,y(1)=3 ?
The solution for (d^2y)/(dt^2)-5(dy)/(dt)+6y=0,y(1)=3 is y=e^{3t-3}(3-e^2c_{2})+c_{2}e^{2t}