What is the solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=0 ?

The solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=0 is y=c_{1}e^{7x}+c_{2}xe^{7x}

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(d^2y)/(dx^2)-14(dy)/(dx)+49y=0

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 0

y = c_{1} e^{7 x} + c_{2} x e^{7 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 0

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} x e^{7 x}

y = c_{1} e^{7 x} + c_{2} x e^{7 x}

\frac{d ^{4} y}{d x ^{4}} - 4 y = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 5

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y^{^{'}} (0) = 2

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = - 5

y^{^{'''}} + 4 y^{^{''}} - 31 y^{^{'}} - 70 y = 0

What is the solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=0 ?
The solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=0 is y=c_{1}e^{7x}+c_{2}xe^{7x}