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Beliebt Rechnen >

y^{''}-y=e^xsin(x)

Lösung

y^{^{''}} - y = e^{x} sin (x)

Lösung

y = c_{1} e^{x} + c_{2} e^{- x} - \frac{1}{5} e^{x} sin (x) - \frac{2}{5} e^{x} cos (x)

Schritte zur Lösung

y^{''} (x) - y = e^{x} sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - \frac{1}{5} e^{x} sin (x) - \frac{2}{5} e^{x} cos (x)

y = c_{1} e^{x} + c_{2} e^{- x} - \frac{1}{5} e^{x} sin (x) - \frac{2}{5} e^{x} cos (x)

Graph

Beliebte Beispiele

4y^{''}-4y^'+y=16e^{(x/2)}

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{(\frac{x}{2})}

(d^2y)/(dx^2)+(dy)/(dx)+7y=e^{5x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 7 y = e^{5 x}

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

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

y^{''}+y= 1/((sin(x))^3)

y^{^{''}} + y = \frac{1}{( sin ( x ) ) ^{3}}

(D^2-4D+4)y=8e^{2x}x^2sin(2x)

(D^{2} - 4 D + 4) y = 8 e^{2 x} x^{2} sin (2 x)