What is the solution for 49y^{''}-y=0,y(0)=0,y^'(0)=1 ?

The solution for 49y^{''}-y=0,y(0)=0,y^'(0)=1 is y= 7/2 e^{t/7}-7/2 e^{-t/7}

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49y^{''}-y=0,y(0)=0,y^'(0)=1

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

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

Solution steps

49 y^{''} (t) - y = 0

Solve linear ODE:

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

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

x^{^{''}} - c x = 0

28 y^{^{''}} + 17 y^{^{'}} - 6 y = 0

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

800 x^{^{''}} + 80 x^{^{'}} - 3 x = 0

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 4, y^{^{'}} (0) = - 7

What is the solution for 49y^{''}-y=0,y(0)=0,y^'(0)=1 ?
The solution for 49y^{''}-y=0,y(0)=0,y^'(0)=1 is y= 7/2 e^{t/7}-7/2 e^{-t/7}