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Beliebt Rechnen >

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

Lösung

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

Lösung

y = (2 - \frac{31}{16}) e^{2 t} + \frac{31}{16} + \frac{3 t}{8}

Schritte zur Lösung

4 y^{''} (t) - 8 y^{'} (t) + 3 = 0

Solve linear ODE:

y = (2 - \frac{31}{16}) e^{2 t} + \frac{31}{16} + \frac{3 t}{8}

y = (2 - \frac{31}{16}) e^{2 t} + \frac{31}{16} + \frac{3 t}{8}

Graph

Beliebte Beispiele

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}}

y^{'''}+3y^{''}-4y=xe^x+14x

y^{^{'''}} + 3 y^{^{''}} - 4 y = x e^{x} + 14 x