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Beliebt Rechnen >

(d^2y)/(dx^2)+y=xsin(2x)

Lösung

\frac{d ^{2} y}{d x ^{2}} + y = x sin (2 x)

Lösung

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x sin ( 2 x )}{3} - \frac{4}{9} cos (2 x)

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + y = x sin (2 x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x sin ( 2 x )}{3} - \frac{4}{9} cos (2 x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{x sin ( 2 x )}{3} - \frac{4}{9} cos (2 x)

Graph

Beliebte Beispiele

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

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

y^{''}-3y^'+2y=4x+3

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x + 3

y^{''}+6y^'+5y=-9e^{2x}

y^{^{''}} + 6 y^{^{'}} + 5 y = - 9 e^{2 x}

y^{''}+18y^'+81y=x,y(0)=0,y^'(0)=0

y^{^{''}} + 18 y^{^{'}} + 81 y = x, y (0) = 0, y^{^{'}} (0) = 0

20y^{''}+9y^'+x=0,y(0)=0,y^'(0)=3

20 y^{^{''}} + 9 y^{^{'}} + x = 0, y (0) = 0, y^{^{'}} (0) = 3