What is the solution for 8t^2y^{''}-16y=11t^2-1 ?

The solution for 8t^2y^{''}-16y=11t^2-1 is y=c_{1}t^2+(c_{2})/t+(66t^2ln(t)-22t^2+9)/(144)

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8t^2y^{''}-16y=11t^2-1

8 t^{2} y^{^{''}} - 16 y = 11 t^{2} - 1

y = c_{1} t^{2} + \frac{c _{2}}{t} + \frac{66 t ^{2} ln ( t ) - 22 t ^{2} + 9}{144}

Solution steps

8 t^{2} y^{''} (t) - 16 y = 11 t^{2} - 1

Solve linear ODE:

y = c_{1} t^{2} + \frac{c _{2}}{t} + \frac{66 t ^{2} ln ( t ) - 22 t ^{2} + 9}{144}

y = c_{1} t^{2} + \frac{c _{2}}{t} + \frac{66 t ^{2} ln ( t ) - 22 t ^{2} + 9}{144}

cot (3 x)

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6

ln (1 + x^{3})

\int - 5 csc^{2} (x) + 5 d x

What is the solution for 8t^2y^{''}-16y=11t^2-1 ?
The solution for 8t^2y^{''}-16y=11t^2-1 is y=c_{1}t^2+(c_{2})/t+(66t^2ln(t)-22t^2+9)/(144)