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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 x sin ( x )}{25} + \frac{4 x cos ( x )}{25} + \frac{4}{125} sin (x) + \frac{22}{125} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 x sin ( x )}{25} + \frac{4 x cos ( x )}{25} + \frac{4}{125} sin (x) + \frac{22}{125} cos (x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 x sin ( x )}{25} + \frac{4 x cos ( x )}{25} + \frac{4}{125} sin (x) + \frac{22}{125} cos (x)

Graph

Beliebte Beispiele

y^{'''}+y^{''}+y^'+y=e^{-t}+14t

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 14 t

y^{^{''}} - 64 y = 16

(d^2y)/(dx^2)+3(dy)/(dx)+2y=sin(e^x)

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

y^{''}+3y^'-10y=x(e^{2x}+1)

y^{^{''}} + 3 y^{^{'}} - 10 y = x (e^{2 x} + 1)

(d^2y)/(dx^2)-y=cosh(x)

\frac{d ^{2} y}{d x ^{2}} - y = cosh (x)