(d^2y)/(dx^2)+2(dy)/(dx)=1+9x^2

Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 1 + 9 x^{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{3 x ^{3}}{2} - \frac{9 x ^{2}}{4} + \frac{11 x}{4}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 1 + 9 x^{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{3 x ^{3}}{2} - \frac{9 x ^{2}}{4} + \frac{11 x}{4}

y = c_{1} + c_{2} e^{- 2 x} + \frac{3 x ^{3}}{2} - \frac{9 x ^{2}}{4} + \frac{11 x}{4}

\int 3 sec^{4} (x) d x

x \to \frac{3 π}{4} lim (- 2 sec (x))

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d er i v a t i v e f (x) = 2 \cdot 7^{2 x^{2} + 3}

\int \frac{( x ^{3} )}{x ^{2} + 25} d x