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Beliebt Rechnen >

y^{''}-ay^'=bx^2

Lösung

y^{^{''}} - a \cdot y^{^{'}} = b \cdot x^{2}

Lösung

y = c_{1} e^{a x} + c_{2} - \frac{b x ^{3}}{3 a} - \frac{b x ^{2}}{a ^{2}} - \frac{2 b x}{a ^{3}}

Schritte zur Lösung

y^{''} (x) - a \cdot y^{'} (x) = b \cdot x^{2}

Solve linear ODE:

y = c_{1} e^{a x} + c_{2} - \frac{b x ^{3}}{3 a} - \frac{b x ^{2}}{a ^{2}} - \frac{2 b x}{a ^{3}}

y = c_{1} e^{a x} + c_{2} - \frac{b x ^{3}}{3 a} - \frac{b x ^{2}}{a ^{2}} - \frac{2 b x}{a ^{3}}

Graph

Beliebte Beispiele

y^{''}+6y^'+2y=e^{-4t}

y^{^{''}} + 6 y^{^{'}} + 2 y = e^{- 4 t}

y^{''}+4y+5y=e^{-t}

y^{^{''}} + 4 y + 5 y = e^{- t}

y^{''}-36y=9e^{6x}

y^{^{''}} - 36 y = 9 e^{6 x}

(d^2y)/(dx^2)+4y=8

\frac{d ^{2} y}{d x ^{2}} + 4 y = 8

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

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