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Beliebt Rechnen >

y^{''}-7y^'+12y=e^3x+e^4x

Lösung

y^{^{''}} - 7 y^{^{'}} + 12 y = e^{3} x + e^{4} x

Lösung

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{( e ^{3} + e ^{4} ) x}{12} + \frac{7 ( e ^{4} + e ^{3} )}{144}

Schritte zur Lösung

y^{''} (x) - 7 y^{'} (x) + 12 y = e^{3} x + e^{4} x

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{( e ^{3} + e ^{4} ) x}{12} + \frac{7 ( e ^{4} + e ^{3} )}{144}

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{( e ^{3} + e ^{4} ) x}{12} + \frac{7 ( e ^{4} + e ^{3} )}{144}

Graph

Beliebte Beispiele

y^{''}+4y^'=10t+1

y^{^{''}} + 4 y^{^{'}} = 10 t + 1

y^{''}+y=cos(x)sec(x)

y^{^{''}} + y = cos (x) sec (x)

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

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

y^{''}+y=t-3sin(2t),y(0)=1,y^'(0)=-3

y^{^{''}} + y = t - 3 sin (2 t), y (0) = 1, y^{^{'}} (0) = - 3

y^{''''}-y=te^t+sin(t)

y^{^{''''}} - y = t e^{t} + sin (t)