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Beliebt Rechnen >

1/2 y^{''}+2y=2tan(2t)-1/2 e^t

Lösung

\frac{1}{2} y^{^{''}} + 2 y = 2 tan (2 t) - \frac{1}{2} e^{t}

Lösung

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{e ^{t} cos ^{2} ( 2 t ) + e ^{t} sin ^{2} ( 2 t ) + 5 cos ( 2 t ) ln ( sec ( 2 t ) + tan ( 2 t ) )}{5}

Schritte zur Lösung

\frac{1}{2} y^{''} (t) + 2 y = 2 tan (2 t) - \frac{1}{2} e^{t}

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{e ^{t} cos ^{2} ( 2 t ) + e ^{t} sin ^{2} ( 2 t ) + 5 cos ( 2 t ) ln ( sec ( 2 t ) + tan ( 2 t ) )}{5}

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{e ^{t} cos ^{2} ( 2 t ) + e ^{t} sin ^{2} ( 2 t ) + 5 cos ( 2 t ) ln ( sec ( 2 t ) + tan ( 2 t ) )}{5}

Graph

Beliebte Beispiele

y^{''}-y=x^2e^x+6

y^{^{''}} - y = x^{2} e^{x} + 6

y^{''}-y=x^2e^x+9

y^{^{''}} - y = x^{2} e^{x} + 9

y^{''}-2y^'-3y=24te^{2t}

y^{^{''}} - 2 y^{^{'}} - 3 y = 24 t e^{2 t}

y^{''}-y^'-6y=-468sin(3t)

y^{^{''}} - y^{^{'}} - 6 y = - 468 sin (3 t)

3y^{''}-4y^'+y=5

3 y^{^{''}} - 4 y^{^{'}} + y = 5