What is the solution for 9(d^2y)/(dx^2)-49y=0,y(0)=1,y^'(0)=0 ?

The solution for 9(d^2y)/(dx^2)-49y=0,y(0)=1,y^'(0)=0 is y=(1-1/2)e^{(7x)/3}+1/2 e^{-(7x)/3}

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9(d^2y)/(dx^2)-49y=0,y(0)=1,y^'(0)=0

9 \frac{d ^{2} y}{d x ^{2}} - 49 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 - \frac{1}{2}) e^{\frac{7 x}{3}} + \frac{1}{2} e^{- \frac{7 x}{3}}

Solution steps

9 y^{''} (x) - 49 y = 0

Solve linear ODE:

y = (1 - \frac{1}{2}) e^{\frac{7 x}{3}} + \frac{1}{2} e^{- \frac{7 x}{3}}

y = (1 - \frac{1}{2}) e^{\frac{7 x}{3}} + \frac{1}{2} e^{- \frac{7 x}{3}}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 y = 0

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} + 6 y = 0

2 y^{^{''}} + 4 y^{^{'}} + 3 y = 0

x^{^{''}} - 0.8 x^{^{'}} + 1.16 x = 0

5 y^{^{''}} + 50 y^{^{'}} + 45 y = 0, y (0) = - 8, y^{^{'}} (0) = 0

What is the solution for 9(d^2y)/(dx^2)-49y=0,y(0)=1,y^'(0)=0 ?
The solution for 9(d^2y)/(dx^2)-49y=0,y(0)=1,y^'(0)=0 is y=(1-1/2)e^{(7x)/3}+1/2 e^{-(7x)/3}