(dx)/(dt)=(6x^2+tsqrt(t^2+x^2))/(6tx)

Lösung

\frac{d x}{d t} = \frac{6 x ^{2} + t t ^{2} + x ^{2}}{6 t x}

x = \frac{ln ^{2} ( t ) + 12 c _{1} ln ( t ) + 36 c _{1}^{2} - 36 t}{6}, x = - \frac{t ln ^{2} ( t ) + 12 c _{1} ln ( t ) + 36 c _{1}^{2} - 36}{6}

Schritte zur Lösung

\frac{d x}{d t} = \frac{6 x ^{2} + t t ^{2} + x ^{2}}{6 t x}

Solve using substitution:

x = \frac{ln ^{2} ( t ) + 12 c _{1} ln ( t ) + 36 c _{1}^{2} - 36 t}{6}, x = - \frac{t ln ^{2} ( t ) + 12 c _{1} ln ( t ) + 36 c _{1}^{2} - 36}{6}

x = \frac{ln ^{2} ( t ) + 12 c _{1} ln ( t ) + 36 c _{1}^{2} - 36 t}{6}, x = - \frac{t ln ^{2} ( t ) + 12 c _{1} ln ( t ) + 36 c _{1}^{2} - 36}{6}

\int_{0}^{3} (- x^{3} + 3 x^{2} - 2) d x

\int (\frac{3}{x ^{5}}) d x

\frac{d}{d x} (e^{- 7 x} cos (7 x))

t an g e n t y = 2 x^{2} + 5, (- 1, 7)

d er i v a t i v e f (x) = x^{2} e^{x} - 2 x e^{x} + 2 e^{x}