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Beliebt Rechnen >

y^{''}+4y=g(t),y(0)=5,y^'(0)=16

Lösung

y^{^{''}} + 4 y = g (t), y (0) = 5, y^{^{'}} (0) = 16

Lösung

y = 5 cos (2 t) + \frac{sin ( 2 t ) ( 64 - g )}{8} + \frac{g t}{4}

Schritte zur Lösung

y^{''} (t) + 4 y = g (t)

Solve linear ODE:

y = 5 cos (2 t) + \frac{sin ( 2 t ) ( 64 - g )}{8} + \frac{g t}{4}

y = 5 cos (2 t) + \frac{sin ( 2 t ) ( 64 - g )}{8} + \frac{g t}{4}

Graph

Beliebte Beispiele

4y^{''}-4y^'+y=16e^{1/2 t}

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{1}{2} t}

16y^{''''}-y=e^{x/2}

16 y^{^{''''}} - y = e^{\frac{x}{2}}

y^{''}+5y^'+6y=36e^t,y(0)=-5,y^'(0)=21

y^{^{''}} + 5 y^{^{'}} + 6 y = 36 e^{t}, y (0) = - 5, y^{^{'}} (0) = 21

y^{''}-6y^'+8y=2x-1

y^{^{''}} - 6 y^{^{'}} + 8 y = 2 x - 1

y^{''}=2y+22cot^3(x),y(0)=11cot(x)

y^{^{''}} = 2 y + 22 cot^{3} (x), y (0) = 11 cot (x)