2(d^2y)/(dx^2)+2(dy)/(dx)+3y=x^2+2x-1

Lösung

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 3 y = x^{2} + 2 x - 1

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{5 x}{2}) + c_{2} sin (\frac{5 x}{2})) + \frac{x ^{2}}{3} + \frac{2 x}{9} - \frac{25}{27}

Schritte zur Lösung

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 3 y = x^{2} + 2 x - 1

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{5 x}{2}) + c_{2} sin (\frac{5 x}{2})) + \frac{x ^{2}}{3} + \frac{2 x}{9} - \frac{25}{27}

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{5 x}{2}) + c_{2} sin (\frac{5 x}{2})) + \frac{x ^{2}}{3} + \frac{2 x}{9} - \frac{25}{27}

y^{^{''}} + y = cos (x) + 3 sin (2 x)

y^{^{''}} + 49 y = x^{2} cos (7 x) + x e^{- 7 x}

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

y^{^{''}} + 7 y^{^{'}} + 10 y = - 10 + e^{4 t}

y^{^{''}} + 2 y^{^{'}} + 2 y = (e^{(- x)}) \cdot cos (x)