What is the solution for y^{''}+36y=6t^2 ?

The solution for y^{''}+36y=6t^2 is y=c_{1}cos(6t)+c_{2}sin(6t)+(t^2)/6-1/108

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y^{''}+36y=6t^2

y^{^{''}} + 36 y = 6 t^{2}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{t ^{2}}{6} - \frac{1}{108}

Solution steps

y^{''} (t) + 36 y = 6 t^{2}

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{t ^{2}}{6} - \frac{1}{108}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{t ^{2}}{6} - \frac{1}{108}

5^{x^{3}}

\frac{( k ^{2} - x ^{2} ) ^{3}}{x ^{2} + a ^{2}}

\int sec (x) tan (x) 1 + sec (x) d x

f (x) = x ∣ x ∣

What is the solution for y^{''}+36y=6t^2 ?
The solution for y^{''}+36y=6t^2 is y=c_{1}cos(6t)+c_{2}sin(6t)+(t^2)/6-1/108