(9y^2-t^2)/(y^5)(dy)/(dt)+t/(2y^4)=0

Lösung

\frac{9 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

y = \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}, y = - - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}

Schritte zur Lösung

\frac{9 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

Solve exact ODE:

y = \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}, y = - - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}

y = \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}, y = - - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}

\frac{d y}{d x} - y = e^{x} \cdot y^{2}

\int \frac{x}{x + 2 y} d x

\frac{d v}{d t} = 2.1 - \frac{7 v}{2180}, v (0) = 0

t an g e n t f (x) = - 2 x^{3}, at x = 2

\frac{d}{d z} (\frac{z ^{2}}{( z - 2 i ) ^{2}})