y^{'''}-7y^{''}=x^2+2cos(x)

Lösung

y^{^{'''}} - 7 y^{^{''}} = x^{2} + 2 cos (x)

y = c_{1} e^{7 x} + c_{2} + c_{3} x - \frac{x ^{4}}{84} - \frac{x ^{3}}{147} - \frac{x ^{2}}{343} - \frac{1}{25} sin (x) + \frac{7}{25} cos (x)

Schritte zur Lösung

y^{'''} (x) - 7 y^{''} (x) = x^{2} + 2 cos (x)

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} + c_{3} x - \frac{x ^{4}}{84} - \frac{x ^{3}}{147} - \frac{x ^{2}}{343} - \frac{1}{25} sin (x) + \frac{7}{25} cos (x)

y = c_{1} e^{7 x} + c_{2} + c_{3} x - \frac{x ^{4}}{84} - \frac{x ^{3}}{147} - \frac{x ^{2}}{343} - \frac{1}{25} sin (x) + \frac{7}{25} cos (x)

y^{^{''}} + y = tan^{2} (t)

y^{^{''''}} + 2 y^{^{''}} + y = 9 + cos (6 t)

y^{^{''}} + y^{^{'}} - 2 y = 2 + 5 cos (2 x)

y^{^{'''}} + 4 y^{^{'}} = tan (x)

y^{^{''}} - 10 y^{^{'}} + 25 y = 25 x + 10