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

Lösung

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = e^{x}

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + \frac{1}{2} e^{x}

Schritte zur Lösung

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = e^{x}

Solve linear ODE:

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + \frac{1}{2} e^{x}

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + \frac{1}{2} e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x + 1

4 x^{^{''}} + x = t^{2} + 2 cos (t)

y^{^{''}} - 4 y + 4 = - 5 e^{3 x}

x^{^{''}} + 4 x = cos (4 t)

x^{^{''}} - 2 x^{^{'}} + 3 x + 2 = 0