What is the solution for y^{''}-14y^'+49y=21x+6 ?

The solution for y^{''}-14y^'+49y=21x+6 is y=c_{1}e^{7x}+c_{2}xe^{7x}+(3x)/7+12/49

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y^{''}-14y^'+49y=21x+6

y^{^{''}} - 14 y^{^{'}} + 49 y = 21 x + 6

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{3 x}{7} + \frac{12}{49}

Solution steps

y^{''} (x) - 14 y^{'} (x) + 49 y = 21 x + 6

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{3 x}{7} + \frac{12}{49}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{3 x}{7} + \frac{12}{49}

What is the solution for y^{''}-14y^'+49y=21x+6 ?
The solution for y^{''}-14y^'+49y=21x+6 is y=c_{1}e^{7x}+c_{2}xe^{7x}+(3x)/7+12/49