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Beliebt Rechnen >

4y^{''}+y=t-cos(t/2)

Lösung

4 y^{^{''}} + y = t - cos (\frac{t}{2})

Lösung

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}) + t - \frac{t sin ( \frac{t}{2} )}{4}

Schritte zur Lösung

4 y^{''} (t) + y = t - cos (\frac{t}{2})

Solve linear ODE:

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}) + t - \frac{t sin ( \frac{t}{2} )}{4}

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}) + t - \frac{t sin ( \frac{t}{2} )}{4}

Graph

Beliebte Beispiele

y^{''}+4y=2e^{2t},y(0)=1,y^'(0)=0

y^{^{''}} + 4 y = 2 e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

y^{''}-y^'-6y=2sin(t)

y^{^{''}} - y^{^{'}} - 6 y = 2 sin (t)

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

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

y^{''}+4y^'+5y=1-5x+8cos(x)-8sin(x)

y^{^{''}} + 4 y^{^{'}} + 5 y = 1 - 5 x + 8 cos (x) - 8 sin (x)

y^{''}+16y=4e^{2t}+4sin(2t)

y^{^{''}} + 16 y = 4 e^{2 t} + 4 sin (2 t)