y^{''}+9y=4(((u^5)/3 pi-u^{13})/(3pi))

Lösung

y^{^{''}} + 9 y = 4 (\frac{\frac{u ^{5}}{3} π - u ^{13}}{3 π})

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{4 ( π u ^{5} - 3 u ^{13} )}{81 π}

Schritte zur Lösung

y^{''} (t) + 9 y = 4 (\frac{\frac{u ^{5}}{3} π - u ^{13}}{3 π})

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{4 ( π u ^{5} - 3 u ^{13} )}{81 π}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{4 ( π u ^{5} - 3 u ^{13} )}{81 π}

y^{^{''}} + y^{^{'}} = sinh (t)

y^{^{''}} - 2 \cdot y^{^{'}} + 2 \cdot y = cos (t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 6 y = t, y (0) = - 3, y^{^{'}} (0) = 0

3 y^{^{''}} + 2 y^{^{'}} + 1 = 0

y^{^{''}} - y^{^{'}} - 6 y = e^{- 3 x} (7 - 8 x + 6 x^{2})