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

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

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

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

y = 1 + \frac{1}{- 1 + 4 e} - \frac{1}{- 1 + 4 e} e^{\frac{t}{4}}

Solution steps

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

Solve linear ODE:

y = 1 + \frac{1}{- 1 + 4 e} - \frac{1}{- 1 + 4 e} e^{\frac{t}{4}}

y = 1 + \frac{1}{- 1 + 4 e} - \frac{1}{- 1 + 4 e} e^{\frac{t}{4}}

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} + 10 y = 0

y^{^{''}} + 8 y^{^{'}} - 65 y = 0

\frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 7 x = 0

y^{^{''}} + (y^{^{'}}) + y = 0

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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