(d^3y)/(dx^3)+(dy)/(dx)=tan(x)

Lösung

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = tan (x)

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) - ln (cos (x)) + cos^{2} (x) + sin (x) (- ln (tan (x) + sec (x)) + sin (x))

Schritte zur Lösung

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = tan (x)

Solve linear ODE:

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) - ln (cos (x)) + cos^{2} (x) + sin (x) (- ln (tan (x) + sec (x)) + sin (x))

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) - ln (cos (x)) + cos^{2} (x) + sin (x) (- ln (tan (x) + sec (x)) + sin (x))

3 x^{^{''}} + 25 x^{^{'}} + 48 x = 5 cos (4 t)

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 39 x e^{x}

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

y^{^{''}} + y = sin (3 x)