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Beliebt Rechnen >

y^{''}-5y^'+4y=2e^x+x+1

Lösung

y^{^{''}} - 5 y^{^{'}} + 4 y = 2 e^{x} + x + 1

Lösung

y = c_{1} e^{4 x} + c_{2} e^{x} - \frac{2 e ^{x} x}{3} + \frac{x}{4} + \frac{9}{16}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) + 4 y = 2 e^{x} + x + 1

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{x} - \frac{2 e ^{x} x}{3} + \frac{x}{4} + \frac{9}{16}

y = c_{1} e^{4 x} + c_{2} e^{x} - \frac{2 e ^{x} x}{3} + \frac{x}{4} + \frac{9}{16}

Graph

Beliebte Beispiele

4y^{''}-8y^'+3=0,y(0)=2,y^'(0)= 1/2

4 y^{^{''}} - 8 y^{^{'}} + 3 = 0, y (0) = 2, y^{^{'}} (0) = \frac{1}{2}

y^{'''}-9y^{''}+27y=3e^{3x}

y^{^{'''}} - 9 y^{^{''}} + 27 y = 3 e^{3 x}

y^{''}+7y^'=x+e^{2x}

y^{^{''}} + 7 y^{^{'}} = x + e^{2 x}

(D^2-1)y=x^2e^{(x^2)/2}

(D^{2} - 1) y = x^{2} e^{\frac{x ^{2}}{2}}

solvefor d,d(x)=(k(x)+18x-9)/(2x^2)

so l v e f or d, d (x) = \frac{k ( x ) + 18 x - 9}{2 x ^{2}}