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Beliebt Rechnen >

y^{''}+4y=t^2+10e^t,y(0)=0,y^'(0)=7

Lösung

y^{^{''}} + 4 y = t^{2} + 10 e^{t}, y (0) = 0, y^{^{'}} (0) = 7

Lösung

y = - \frac{15}{8} cos (2 t) + \frac{5}{2} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + 2 e^{t}

Schritte zur Lösung

y^{''} (t) + 4 y = t^{2} + 10 e^{t}

Solve linear ODE:

y = - \frac{15}{8} cos (2 t) + \frac{5}{2} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + 2 e^{t}

y = - \frac{15}{8} cos (2 t) + \frac{5}{2} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + 2 e^{t}

Graph

Beliebte Beispiele

y^{''}-2y^'-3y=-3e^{-x}

y^{^{''}} - 2 y^{^{'}} - 3 y = - 3 e^{- x}

x^{''}+2x^'+7x=6cos(2t)

x^{^{''}} + 2 x^{^{'}} + 7 x = 6 cos (2 t)

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

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

y^{'''}-y^{''}=4x+2xe^{-2x}

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

y^{''}-8y^'+16y=4e^{4x}ln(x)

y^{^{''}} - 8 y^{^{'}} + 16 y = 4 e^{4 x} ln (x)