What is the solution for y^{'''}-5y^{''}+6y^'=6e^x,y(0)=18 ?

The solution for y^{'''}-5y^{''}+6y^'=6e^x,y(0)=18 is y=15-c_{2}-c_{3}+c_{2}e^{2x}+c_{3}e^{3x}+3e^x

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y^{'''}-5y^{''}+6y^'=6e^x,y(0)=18

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{x}, y (0) = 18

y = 15 - c_{2} - c_{3} + c_{2} e^{2 x} + c_{3} e^{3 x} + 3 e^{x}

Solution steps

y^{'''} (x) - 5 y^{''} (x) + 6 y^{'} (x) = 6 e^{x}

Solve linear ODE:

y = 15 - c_{2} - c_{3} + c_{2} e^{2 x} + c_{3} e^{3 x} + 3 e^{x}

y = 15 - c_{2} - c_{3} + c_{2} e^{2 x} + c_{3} e^{3 x} + 3 e^{x}

What is the solution for y^{'''}-5y^{''}+6y^'=6e^x,y(0)=18 ?
The solution for y^{'''}-5y^{''}+6y^'=6e^x,y(0)=18 is y=15-c_{2}-c_{3}+c_{2}e^{2x}+c_{3}e^{3x}+3e^x