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Beliebt Rechnen >

y^{''}+y=2x*sin(x)

Lösung

y^{^{''}} + y = 2 x \cdot sin (x)

Lösung

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

Schritte zur Lösung

y^{''} (x) + y = 2 x \cdot sin (x)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

2y^{''}-4y^'+3y=2e^{3x}-6

2 y^{^{''}} - 4 y^{^{'}} + 3 y = 2 e^{3 x} - 6

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

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

y^{''}+9y^'+8y=3e^{5x}

y^{^{''}} + 9 y^{^{'}} + 8 y = 3 e^{5 x}

y^{''}-6y^'+25y=2sin(t)-cos(t)

y^{^{''}} - 6 y^{^{'}} + 25 y = 2 sin (t) - cos (t)

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

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