(dy)/(dx)+ln((x+1)^{y/x})=x^3y^1

Lösung

\frac{d y}{d x} + ln ((x + 1)^{\frac{y}{x}}) = x^{3} y^{1}

y = e^{\int \frac{x ^{4} - l n ( x + 1 )}{x} d x}

Schritte zur Lösung

\frac{d y}{d x} + ln ((x + 1)^{\frac{y}{x}}) = x^{3} y^{1}

Solve separable ODE:

y = e^{\int \frac{x ^{4} - l n ( x + 1 )}{x} d x}

y = e^{\int \frac{x ^{4} - l n ( x + 1 )}{x} d x}

\frac{d y}{d x} = x^{3} e^{- y}

x^{^{'}} = - \frac{1}{2} x

\frac{d v}{d t} = 30 - \frac{9}{100} v

2 (x - 1) d x + 3 y^{2} d y = 0, y (2) = 1

y y^{^{'}} + y^{^{'}} = x, y (2) = 2