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Beliebt Rechnen >

y^{''}+15y^'+7y=sin(x)+cos(x)

Lösung

y^{^{''}} + 15 y^{^{'}} + 7 y = sin (x) + cos (x)

Lösung

y = c_{1} e^{\frac{( - 15 + 197 ) x}{2}} + c_{2} e^{\frac{( - 15 - 197 ) x}{2}} + \frac{7}{87} sin (x) - \frac{1}{29} cos (x)

Schritte zur Lösung

y^{''} (x) + 15 y^{'} (x) + 7 y = sin (x) + cos (x)

Solve linear ODE:

y = c_{1} e^{\frac{( - 15 + 197 ) x}{2}} + c_{2} e^{\frac{( - 15 - 197 ) x}{2}} + \frac{7}{87} sin (x) - \frac{1}{29} cos (x)

y = c_{1} e^{\frac{( - 15 + 197 ) x}{2}} + c_{2} e^{\frac{( - 15 - 197 ) x}{2}} + \frac{7}{87} sin (x) - \frac{1}{29} cos (x)

Graph

Beliebte Beispiele

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

(y^{^{''}}) - 2 y^{^{'}} + y = \frac{e ^{x}}{1 + x ^{2}}

y^{''}+2y^'+2y=t^2

y^{^{''}} + 2 y^{^{'}} + 2 y = t^{2}

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

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

y^{''}+4y^'+6y=1^{-t}

y^{^{''}} + 4 y^{^{'}} + 6 y = 1^{- t}

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

y^{^{''}} + y = t - \frac{π}{2}, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 1