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

The solution for 4y^{''}-5y^'+y=0,y(0)=4 is y=(4-c_{2})e^t+c_{2}e^{t/4}

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

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

y = (4 - c_{2}) e^{t} + c_{2} e^{\frac{t}{4}}

Solution steps

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

Solve linear ODE:

y = (4 - c_{2}) e^{t} + c_{2} e^{\frac{t}{4}}

y = (4 - c_{2}) e^{t} + c_{2} e^{\frac{t}{4}}

What is the solution for 4y^{''}-5y^'+y=0,y(0)=4 ?
The solution for 4y^{''}-5y^'+y=0,y(0)=4 is y=(4-c_{2})e^t+c_{2}e^{t/4}