(dy)/(dt)=-0.7654sqrt(y)

Lösung

\frac{d y}{d t} = - 0.7654 y

y = \frac{0.58583716 t ^{2}}{4} - \frac{1.5308 c _{1} t}{4} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

\frac{d y}{d t} = - 0.7654 y

Solve separable ODE:

y = \frac{0.58583716 t ^{2}}{4} - \frac{1.5308 c _{1} t}{4} + \frac{c _{1}^{2}}{4}

y = \frac{0.58583716 t ^{2}}{4} - \frac{1.5308 c _{1} t}{4} + \frac{c _{1}^{2}}{4}

y^{5} \frac{d y}{d x} = 5 x^{3} y^{6} - 15 x^{3}

\frac{( 9 + x ^{2} ) d y}{d x} - x y = x

y^{^{'}} = \frac{5 x ^{2} - 1}{5 + 6 y}

2 x y^{^{'}} + x^{2} y = 0

y^{^{'}} = \frac{x + x y ^{2}}{4 x}