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Beliebt Rechnen >

(d^2y)/(dx^2)-10(dy)/(dx)+25y=30*x+3

Lösung

\frac{d ^{2} y}{d x ^{2}} - 10 \cdot \frac{d y}{d x} + 25 \cdot y = 30 \cdot x + 3

Lösung

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 10 \cdot \frac{d y}{d x} + 25 \cdot y = 30 \cdot x + 3

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-5y^'=28xe^{-2x}+10

y^{^{''}} - 5 y^{^{'}} = 28 x e^{- 2 x} + 10

2x^{''}+5x^'+2x=10sin(t)

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 10 sin (t)

y^{''}-4y^'-12y=3e^5t

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 e^{5} t

y^{'''}-4y^{''}-y^'+4y=e^{6x}

y^{^{'''}} - 4 y^{^{''}} - y^{^{'}} + 4 y = e^{6 x}

y^{''}-4y^'+5y=12e^t,y(0)=6,y^'(0)=7

y^{^{''}} - 4 y^{^{'}} + 5 y = 12 e^{t}, y (0) = 6, y^{^{'}} (0) = 7