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Beliebt Rechnen >

y^{''}-4y^'+4y=xe^{2x}+x^3e^{2x}

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = x e^{2 x} + x^{3} e^{2 x}

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{3}}{6} + \frac{e ^{2 x} x ^{5}}{20}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = x e^{2 x} + x^{3} e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{3}}{6} + \frac{e ^{2 x} x ^{5}}{20}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{3}}{6} + \frac{e ^{2 x} x ^{5}}{20}

Graph

Beliebte Beispiele

y^{''}-11y^'+10y=2x^2-44x+4

y^{^{''}} - 11 y^{^{'}} + 10 y = 2 x^{2} - 44 x + 4

y^{''}+9y=11sec^2(3t)

y^{^{''}} + 9 y = 11 sec^{2} (3 t)

y^{''}-y^'=ex(10+x^2)

y^{^{''}} - y^{^{'}} = e x (10 + x^{2})

y^{''}+9y= 1/9 sin(x)

y^{^{''}} + 9 y = \frac{1}{9} sin (x)

y^{'''}-5y^{''}+6y^'=7+7sin(x)

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 7 + 7 sin (x)