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Beliebt Rechnen >

y^{''}+y^'=cos(x),y(0)=0,y^'(0)=1

Lösung

y^{^{''}} + y^{^{'}} = cos (x), y (0) = 0, y^{^{'}} (0) = 1

Lösung

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

Schritte zur Lösung

y^{''} (x) + y^{'} (x) = cos (x)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

4y^{''}-y=e^{(x/2)}+5

4 y^{^{''}} - y = e^{(\frac{x}{2})} + 5

x^{''}+64x=sin(5t)

x^{^{''}} + 64 x = sin (5 t)

0.5y^{''}+50y=cos(t)

0.5 y^{^{''}} + 50 y = cos (t)

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

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

(d^2y)/(dx^2)-4y^'+3y=8e^{-x}+9

\frac{d ^{2} y}{d x ^{2}} - 4 y^{^{'}} + 3 y = 8 e^{- x} + 9