What is the solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=0 ?

The solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=0 is y=c_{1}e^x+c_{2}e^{x/3}

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3(d^2y)/(dx^2)-4(dy)/(dx)+y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} + 12 y = 0

9 y^{^{''}} + 36 y^{^{'}} + 100 y = 0, y (1) = 4, y^{^{'}} (1) = 9

y^{^{''}} = 8 y^{^{'}} - 15 y

y^{^{''}} - y^{^{'}} + a y = 0

y^{^{''''}} - 36 y^{^{'''}} + 324 y^{^{''}} = 0

What is the solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=0 ?
The solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=0 is y=c_{1}e^x+c_{2}e^{x/3}