(dy)/(dx)(x^2+2)+4x(y^2+2y+1)=0

Lösung

\frac{d y}{d x} (x^{2} + 2) + 4 x (y^{2} + 2 y + 1) = 0

y = - \frac{1}{- 2 ln ( x ^{2} + 2 ) + c _{1}} + \frac{2 ln ( x ^{2} + 2 )}{- 2 ln ( x ^{2} + 2 ) + c _{1}} - \frac{c _{1}}{- 2 ln ( x ^{2} + 2 ) + c _{1}}

Schritte zur Lösung

\frac{d y}{d x} (x^{2} + 2) + 4 x (y^{2} + 2 y + 1) = 0

Solve separable ODE:

y = - \frac{1}{- 2 ln ( x ^{2} + 2 ) + c _{1}} + \frac{2 ln ( x ^{2} + 2 )}{- 2 ln ( x ^{2} + 2 ) + c _{1}} - \frac{c _{1}}{- 2 ln ( x ^{2} + 2 ) + c _{1}}

y = - \frac{1}{- 2 ln ( x ^{2} + 2 ) + c _{1}} + \frac{2 ln ( x ^{2} + 2 )}{- 2 ln ( x ^{2} + 2 ) + c _{1}} - \frac{c _{1}}{- 2 ln ( x ^{2} + 2 ) + c _{1}}

x \cdot \frac{d y}{d x} = 3 y

\frac{d p}{d x} = p

\frac{d x}{d t} = 0.1 x - 186

\frac{d Q}{d t} = 300 + 6 Q

y^{^{'}} = \frac{3 t ^{2} y}{y + 1}, y (2) = 1