(dx)/(dt)=(7x^2+3tsqrt(8t^2+x^2))/(7tx)

Lösung

\frac{d x}{d t} = \frac{7 x ^{2} + 3 t 8 t ^{2} + x ^{2}}{7 t x}

x = \frac{9 ln ^{2} ( t ) + 42 c _{1} ln ( t ) + 49 c _{1}^{2} - 392 t}{7}, x = - \frac{t 9 ln ^{2} ( t ) + 42 c _{1} ln ( t ) + 49 c _{1}^{2} - 392}{7}

Schritte zur Lösung

\frac{d x}{d t} = \frac{7 x ^{2} + 3 t 8 t ^{2} + x ^{2}}{7 t x}

Solve using substitution:

x = \frac{9 ln ^{2} ( t ) + 42 c _{1} ln ( t ) + 49 c _{1}^{2} - 392 t}{7}, x = - \frac{t 9 ln ^{2} ( t ) + 42 c _{1} ln ( t ) + 49 c _{1}^{2} - 392}{7}

x = \frac{9 ln ^{2} ( t ) + 42 c _{1} ln ( t ) + 49 c _{1}^{2} - 392 t}{7}, x = - \frac{t 9 ln ^{2} ( t ) + 42 c _{1} ln ( t ) + 49 c _{1}^{2} - 392}{7}

\int t \cdot ln (t) d t

t an g e n t 2 x^{3} - 3 x^{2} - 72 x + 2

in v erse l a pl a ce \frac{s + 1}{s ^{2} - 4 s}

d er i v a t i v e 2 \cdot e^{x^{2} - 4 x}

\int 2 x - 5 d x