(d^2y)/(dx^2)=sqrt(2x-3)

Lösung

\frac{d ^{2} y}{d x ^{2}} = 2 x - 3

y = \frac{1}{15} (2 x - 3)^{\frac{5}{2}} + c_{1} x + c_{2}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} = 2 x - 3

Ersetze

\frac{d ^{2} y}{d x ^{2}}

mit

y^{''} (x)

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

Löse

y^{''} (x) = 2 x - 3 : y^{'} (x) = \frac{1}{3} (2 x - 3)^{\frac{3}{2}} + c_{1}

Löse

y^{'} (x) = \frac{1}{3} (2 x - 3)^{\frac{3}{2}} + c_{1} : y = \frac{1}{15} (2 x - 3)^{\frac{5}{2}} + c_{1} x + c_{2}

y = \frac{1}{15} (2 x - 3)^{\frac{5}{2}} + c_{1} x + c_{2}

x \to 0 lim (x^{4} sin (\frac{3}{x}))

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\frac{d}{d x} (x^{3} + a x^{2} y + b x y^{2} + y^{3})