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Beliebt Rechnen >

y^{''}-6y^'+13y=e^{3x}cos(2x)

Lösung

y^{^{''}} - 6 y^{^{'}} + 13 y = e^{3 x} cos (2 x)

Lösung

y = e^{3 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{e ^{3 x} x sin ( 2 x )}{4}

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 13 y = e^{3 x} cos (2 x)

Solve linear ODE:

y = e^{3 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{e ^{3 x} x sin ( 2 x )}{4}

y = e^{3 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{e ^{3 x} x sin ( 2 x )}{4}

Graph

Beliebte Beispiele

y=5(d^2x)/(dy^2)+3(dx)/(dy)

y = 5 \frac{d ^{2} x}{d y ^{2}} + 3 \frac{d x}{d y}

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

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

y^{''}-4y^'+4y=8

y^{^{''}} - 4 y^{^{'}} + 4 y = 8

y^{''}-y^'-6y=14sin(3x)

y^{^{''}} - y^{^{'}} - 6 y = 14 sin (3 x)

(d^2y)/(dx^2)+2(dy)/(dx)-15y=7+4x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = 7 + 4 x