What is the solution for y^{''}-y^'+1/4 y=0,y(0)=2,y^'(0)=2 ?

The solution for y^{''}-y^'+1/4 y=0,y(0)=2,y^'(0)=2 is y=2e^{t/2}+e^{t/2}t

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y^{''}-y^'+1/4 y=0,y(0)=2,y^'(0)=2

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 0, y (0) = 2, y^{^{'}} (0) = 2

y = 2 e^{\frac{t}{2}} + e^{\frac{t}{2}} t

Solution steps

y^{''} (t) - y^{'} (t) + \frac{1}{4} y = 0

Solve linear ODE:

y = 2 e^{\frac{t}{2}} + e^{\frac{t}{2}} t

y = 2 e^{\frac{t}{2}} + e^{\frac{t}{2}} t

What is the solution for y^{''}-y^'+1/4 y=0,y(0)=2,y^'(0)=2 ?
The solution for y^{''}-y^'+1/4 y=0,y(0)=2,y^'(0)=2 is y=2e^{t/2}+e^{t/2}t