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Beliebt Rechnen >

y^{'''}+4y^'=e^x+3sin(2x)+1

Lösung

y^{^{'''}} + 4 y^{^{'}} = e^{x} + 3 sin (2 x) + 1

Lösung

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{5} e^{x} - \frac{3 x sin ( 2 x )}{8} + \frac{x}{4}

Schritte zur Lösung

y^{'''} (x) + 4 y^{'} (x) = e^{x} + 3 sin (2 x) + 1

Solve linear ODE:

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{5} e^{x} - \frac{3 x sin ( 2 x )}{8} + \frac{x}{4}

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{5} e^{x} - \frac{3 x sin ( 2 x )}{8} + \frac{x}{4}

Graph

Beliebte Beispiele

5y^{''}+6y^'+25y=4cos(2t)

5 y^{^{''}} + 6 y^{^{'}} + 25 y = 4 cos (2 t)

y^{''}+y^'=3,x^2y(0)=0,y^'(0)=1

y^{^{''}} + y^{^{'}} = 3, x^{2} y (0) = 0, y^{^{'}} (0) = 1

y^{''}-2y^'-7y=1e^{5t}

y^{^{''}} - 2 y^{^{'}} - 7 y = 1 e^{5 t}

9y^{''}+4y^'-y=22

9 y^{^{''}} + 4 y^{^{'}} - y = 22

x^{''}+4x=12*cos(t)

x^{^{''}} + 4 x = 12 \cdot cos (t)