y^{''}-10y^'+25y=e^5xln(4+x^2)

Lösung

y^{^{''}} - 10 y^{^{'}} + 25 y = e^{5} x ln (4 + x^{2})

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + e^{5 x} \cdot \int - e^{- 5 x + 5} x^{2} ln (4 + x^{2}) d x + e^{5 x} x \cdot \int e^{- 5 x + 5} x ln (4 + x^{2}) d x

Schritte zur Lösung

y^{''} (x) - 10 y^{'} (x) + 25 y = e^{5} x ln (4 + x^{2})

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + e^{5 x} \cdot \int - e^{- 5 x + 5} x^{2} ln (4 + x^{2}) d x + e^{5 x} x \cdot \int e^{- 5 x + 5} x ln (4 + x^{2}) d x

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + e^{5 x} \cdot \int - e^{- 5 x + 5} x^{2} ln (4 + x^{2}) d x + e^{5 x} x \cdot \int e^{- 5 x + 5} x ln (4 + x^{2}) d x

\frac{d ^{2} y}{d x ^{2}} + y = cot (x)

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- t}

x^{^{''}} + 5 x^{^{'}} + 4 x = 5 e^{10 t}

\frac{d ^{2} y}{d x ^{2}} + y = 1

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