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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{7}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{7}{8}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{7}{8}

Graph

Beliebte Beispiele

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)

y^{''}-6y+y^'=e^x

y^{^{''}} - 6 y + y^{^{'}} = e^{x}

y^{''}-4y=-12sin(2t)

y^{^{''}} - 4 y = - 12 sin (2 t)