y^{''}-2y^'-7y=3x^2

Lösung

y^{^{''}} - 2 y^{^{'}} - 7 y = 3 x^{2}

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) x} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) x} - \frac{3 x ^{2}}{7} + \frac{12 x}{49} - \frac{66}{343}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) - 7 y = 3 x^{2}

Solve linear ODE:

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) x} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) x} - \frac{3 x ^{2}}{7} + \frac{12 x}{49} - \frac{66}{343}

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) x} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) x} - \frac{3 x ^{2}}{7} + \frac{12 x}{49} - \frac{66}{343}

1 y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{x ^{2}}

y^{^{''}} + y^{^{'}} - 20 y = 3 e^{t}

y^{^{''}} - 4 y = 4 x - 4

y^{^{''}} + 2 y^{^{'}} = 8 x^{3}

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} \cdot sin (x)