What is the solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=x-7 ?

The solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=x-7 is y=c_{1}e^x+c_{2}e^{x/3}+x-3

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3(d^2y)/(dx^2)-4(dy)/(dx)+y=x-7

3 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + y = x - 7

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

Solution steps

3 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + y = x - 7

Solve linear ODE:

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

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

What is the solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=x-7 ?
The solution for 3(d^2y)/(dx^2)-4(dy)/(dx)+y=x-7 is y=c_{1}e^x+c_{2}e^{x/3}+x-3