What is the solution for (d^2+9)y=7e^{3x}+3x^2+4 ?

The solution for (d^2+9)y=7e^{3x}+3x^2+4 is y=c_{1}cos(3x)+c_{2}sin(3x)+7/18 e^{3x}+(x^2)/3+10/27

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(d^2+9)y=7e^{3x}+3x^2+4

(d^{2} + 9) y = 7 e^{3 x} + 3 x^{2} + 4

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{7}{18} e^{3 x} + \frac{x ^{2}}{3} + \frac{10}{27}

Solution steps

(d^{2} + 9) y = 7 e^{3 x} + 3 x^{2} + 4

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{7}{18} e^{3 x} + \frac{x ^{2}}{3} + \frac{10}{27}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{7}{18} e^{3 x} + \frac{x ^{2}}{3} + \frac{10}{27}

y^{^{''}} - 2 y^{^{'}} + y = (3 x + 1) e^{x}

(d^{2} - 13 d + 12) \cdot y = x

(d - 1)^{2} \cdot y = e^{x} \cdot sec^{2} (x) tan (x)

y^{^{''}} + y^{^{'}} - 2 y = 20 sin (2 x)

(d^{2} + 3 d + 2) y = sin (e^{x})

What is the solution for (d^2+9)y=7e^{3x}+3x^2+4 ?
The solution for (d^2+9)y=7e^{3x}+3x^2+4 is y=c_{1}cos(3x)+c_{2}sin(3x)+7/18 e^{3x}+(x^2)/3+10/27