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Beliebt Rechnen >

4y^{''}-4y^'+y=80e^{t/2}

Lösung

4 y^{^{''}} - 4 y^{^{'}} + y = 80 e^{\frac{t}{2}}

Lösung

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 10 e^{\frac{t}{2}} t^{2}

Schritte zur Lösung

4 y^{''} (t) - 4 y^{'} (t) + y = 80 e^{\frac{t}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 10 e^{\frac{t}{2}} t^{2}

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{\frac{t}{2}} t + 10 e^{\frac{t}{2}} t^{2}

Graph

Beliebte Beispiele

-2y^{''}+y=e^{-0.2x},y(0)=1,y^'(1)=-y(1)

- 2 y^{^{''}} + y = e^{- 0.2 x}, y (0) = 1, y^{^{'}} (1) = - y (1)

y^{''}-64y=sinh(8x)

y^{^{''}} - 64 y = sinh (8 x)

y^{''}-y^'-2y=-2x^3+x^2+4x+1

y^{^{''}} - y^{^{'}} - 2 y = - 2 x^{3} + x^{2} + 4 x + 1

y^{''}-4y^'+3y=xe^{2x}

y^{^{''}} - 4 y^{^{'}} + 3 y = x e^{2 x}

y^{''}+4y=3sin(x)+5cos(3x)

y^{^{''}} + 4 y = 3 sin (x) + 5 cos (3 x)