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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(d^2y)/(dx^2)-y=sin(x)+e^{-5x}

\frac{d ^{2} y}{d x ^{2}} - y = sin (x) + e^{- 5 x}

y^{''}-5y^'+6y=2xe^{3x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x e^{3 x}

y^{''}-4y^'+3y=1

y^{^{''}} - 4 y^{^{'}} + 3 y = 1

y^{''}-32y=16cos(x)

y^{^{''}} - 32 y = 16 cos (x)

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

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