What is the solution for 49y^{''}-81y=0,y(0)=1,y^'(0)=0 ?

The solution for 49y^{''}-81y=0,y(0)=1,y^'(0)=0 is y=(1-1/2)e^{(9t)/7}+1/2 e^{-(9t)/7}

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49y^{''}-81y=0,y(0)=1,y^'(0)=0

49 y^{^{''}} - 81 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 - \frac{1}{2}) e^{\frac{9 t}{7}} + \frac{1}{2} e^{- \frac{9 t}{7}}

Solution steps

49 y^{''} (t) - 81 y = 0

Solve linear ODE:

y = (1 - \frac{1}{2}) e^{\frac{9 t}{7}} + \frac{1}{2} e^{- \frac{9 t}{7}}

y = (1 - \frac{1}{2}) e^{\frac{9 t}{7}} + \frac{1}{2} e^{- \frac{9 t}{7}}

y^{^{''}} + 36 y = 0, y (0) = 4, y^{^{'}} (0) = - 4

y^{^{''''''}} - 64 y = 0

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

x^{^{''}} - x^{^{'}} - 1 = - 1

y^{^{''}} - y^{^{'}} - 30 y = 0, y (0) = 0, y^{^{'}} (0) = 5

What is the solution for 49y^{''}-81y=0,y(0)=1,y^'(0)=0 ?
The solution for 49y^{''}-81y=0,y(0)=1,y^'(0)=0 is y=(1-1/2)e^{(9t)/7}+1/2 e^{-(9t)/7}