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Beliebt Rechnen >

y^{''}-3y^'+2y=t-2,y(0)=0,y^'(0)=1

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = t - 2, y (0) = 0, y^{^{'}} (0) = 1

Lösung

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

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + 2 y = t - 2

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-6y^'+5y=e^{2t}*3

y^{^{''}} - 6 y^{^{'}} + 5 y = e^{2 t} \cdot 3

y^{''}-4y^'+4y=x^2+2

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{2} + 2

y^{''}+9y^'=e^x,y(0)=0,y^'(0)=0

y^{^{''}} + 9 y^{^{'}} = e^{x}, y (0) = 0, y^{^{'}} (0) = 0

3y^{''}-5y^'+y=x^2+1+sin(2x)

3 y^{^{''}} - 5 y^{^{'}} + y = x^{2} + 1 + sin (2 x)

y^{''}-y^'-6y=6cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 6 cos (3 x)