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Beliebt Rechnen >

y^{''}-3y^'+2y=x,y(0)=e^x

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = x, y (0) = e^{x}

Lösung

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x}{2} + \frac{3}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x}{2} + \frac{3}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x}{2} + \frac{3}{4}

Graph

Beliebte Beispiele

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

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

-3y^{''}-2y^'+y=t^2+t-2e^{2t}

- 3 y^{^{''}} - 2 y^{^{'}} + y = t^{2} + t - 2 e^{2 t}

x^{'''}-4x^{''}+5x^'-2x=2t+3

x^{^{'''}} - 4 x^{^{''}} + 5 x^{^{'}} - 2 x = 2 t + 3

y^{''}+4y=sin(2x+3)

y^{^{''}} + 4 y = sin (2 x + 3)

(d^2+2d+2)y=3e^xsin(x)

(d^{2} + 2 d + 2) y = 3 e^{x} sin (x)