What is the solution for (d^2y)/(dx^2)-10(dy)/(dx)+21y=0 ?

The solution for (d^2y)/(dx^2)-10(dy)/(dx)+21y=0 is y=c_{1}e^{7x}+c_{2}e^{3x}

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(d^2y)/(dx^2)-10(dy)/(dx)+21y=0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 21 y = 0

y = c_{1} e^{7 x} + c_{2} e^{3 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 21 y = 0

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{3 x}

y = c_{1} e^{7 x} + c_{2} e^{3 x}

(D^{2} + 2)^{3} (D^{2} - 3)^{2} y = 0

y^{^{'''}} + 3 y^{^{''}} - 5 y^{^{'}} - 39 y = 0, y (0) = e^{3 x}

(D^{2} + 1)^{3} y = 0

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 4 y = 0

What is the solution for (d^2y)/(dx^2)-10(dy)/(dx)+21y=0 ?
The solution for (d^2y)/(dx^2)-10(dy)/(dx)+21y=0 is y=c_{1}e^{7x}+c_{2}e^{3x}