(dy}{dx}=\frac{y^2+1)/x ,y(pi/4)=1

Lösung

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

y = tan (ln (x) + \frac{π}{4} - ln (\frac{π}{4}))

Schritte zur Lösung

\frac{d y}{d x} = \frac{y ^{2} + 1}{x}

Solve separable ODE:

y = tan (ln (x) + \frac{π}{4} - ln (\frac{π}{4}))

y = tan (ln (x) + \frac{π}{4} - ln (\frac{π}{4}))

y^{^{'}} = x^{2} \cdot y^{2}

y^{^{'}} = e^{- y} \frac{x ^{4}}{8}

5 y^{2} d x - 45 x y d y = 0

\frac{d y}{d x} = - 0.3 y

2 y y^{^{'}} = 3 t^{2}, y (0) = 8