What is the solution for y^{''}+y^'+y/4 =0,y(0)=0,y^'(0)=7 ?

The solution for y^{''}+y^'+y/4 =0,y(0)=0,y^'(0)=7 is y=7e^{-t/2}t

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y^{''}+y^'+y/4 =0,y(0)=0,y^'(0)=7

y^{^{''}} + y^{^{'}} + \frac{y}{4} = 0, y (0) = 0, y^{^{'}} (0) = 7

y = 7 e^{- \frac{t}{2}} t

Solution steps

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

Solve linear ODE:

y = 7 e^{- \frac{t}{2}} t

y = 7 e^{- \frac{t}{2}} t

y^{^{'''}} + 10 y^{^{''}} + 27 y^{^{'}} + 18 y = 0

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

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

q^{^{''}} + 90 q^{^{'}} + 1500 q = 0

\frac{d ^{2} x}{d t ^{2}} + 48 x = 0

What is the solution for y^{''}+y^'+y/4 =0,y(0)=0,y^'(0)=7 ?
The solution for y^{''}+y^'+y/4 =0,y(0)=0,y^'(0)=7 is y=7e^{-t/2}t