What is the solution for a(d^2y)/(dx^2)-yb^2=0 ?

The solution for a(d^2y)/(dx^2)-yb^2=0 is y=c_{1}e^{(bx)/(sqrt(a))}+c_{2}e^{-(bx)/(sqrt(a))}

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a(d^2y)/(dx^2)-yb^2=0

a \frac{d ^{2} y}{d x ^{2}} - y b^{2} = 0

y = c_{1} e^{\frac{b x}{a}} + c_{2} e^{- \frac{b x}{a}}

Solution steps

a \frac{d ^{2} y}{d x ^{2}} - y b^{2} = 0

Solve linear ODE:

y = c_{1} e^{\frac{b x}{a}} + c_{2} e^{- \frac{b x}{a}}

y = c_{1} e^{\frac{b x}{a}} + c_{2} e^{- \frac{b x}{a}}

4 y^{^{''}} + 28 y^{^{'}} + 49 y = 0, y (0) = 1, y^{^{'}} (0) = - 6

14 y^{^{''}} + 5 y^{^{'}} - 6 y = 0

y^{^{''}} - 24 y^{^{'}} + 10 y = 0

y^{^{''}} = 5 y, y (0) = - 2, y (2) = 10

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 7, y^{^{'}} (0) = 4

What is the solution for a(d^2y)/(dx^2)-yb^2=0 ?
The solution for a(d^2y)/(dx^2)-yb^2=0 is y=c_{1}e^{(bx)/(sqrt(a))}+c_{2}e^{-(bx)/(sqrt(a))}