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

The solution for 4y^{''}+y^'=0,y(0)=1,y^'(0)=-1 is y=4e^{-t/4}-3

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

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

y = 4 e^{- \frac{t}{4}} - 3

Solution steps

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

Solve linear ODE:

y = 4 e^{- \frac{t}{4}} - 3

y = 4 e^{- \frac{t}{4}} - 3

y^{^{''}} + 13 y^{^{'}} = 0

x^{^{''}} + x^{^{'}} + 1000 x = 0

y^{^{''}} + 14 y^{^{'}} + 50 y = 0, y (0) = - 5, y^{^{'}} (0) = 5

v^{^{''}} + 3 v^{^{'}} + 2 v = 0

y^{^{''}} + 43 y^{^{'}} + 8 y = 0

What is the solution for 4y^{''}+y^'=0,y(0)=1,y^'(0)=-1 ?
The solution for 4y^{''}+y^'=0,y(0)=1,y^'(0)=-1 is y=4e^{-t/4}-3