What is the solution for y^{''}-y^'+0.25y=0,y(0)=2,y^'(0)=2 ?

The solution for y^{''}-y^'+0.25y=0,y(0)=2,y^'(0)=2 is y=2e^{t/2}+e^{t/2}t

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y^{''}-y^'+0.25y=0,y(0)=2,y^'(0)=2

y^{^{''}} - y^{^{'}} + 0.25 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) + 0.25 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

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

2 y^{^{''}} + 10 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = 0, y (0) = 5

2 y^{^{''}} - 4 y^{^{'}} + 5 y = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 63 y = 0

25 y^{^{''}} + 80 y^{^{'}} + 64 y = 0, y (0) = 8

What is the solution for y^{''}-y^'+0.25y=0,y(0)=2,y^'(0)=2 ?
The solution for y^{''}-y^'+0.25y=0,y(0)=2,y^'(0)=2 is y=2e^{t/2}+e^{t/2}t