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Beliebt Rechnen >

(d^2-1)y=xe^x+cos^2(x)+x^2

Lösung

(d^{2} - 1) \cdot y = x \cdot e^{x} + cos^{2} (x) + x^{2}

Lösung

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

Schritte zur Lösung

(d^{2} - 1) y = x e^{x} + cos^{2} (x) + x^{2}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+2y^'+y=8e^x,y(0)=0,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + y = 8 e^{x}, y (0) = 0, y^{^{'}} (0) = 0

y^{''}-2y^'+2y=x^2+1

y^{^{''}} - 2 y^{^{'}} + 2 y = x^{2} + 1

y^{''}-y^'= 1/(e^x+1)

y^{^{''}} - y^{^{'}} = \frac{1}{e ^{x} + 1}

y^{''}-10y^'+25y=3e^{5t}

y^{^{''}} - 10 y^{^{'}} + 25 y = 3 e^{5 t}

y^{''}+y=\H(t-1)

y^{^{''}} + y = H (t - 1)