9ty+e^ty^'= y/(t^2+81)

Lösung

9 t y + e^{t} y^{^{'}} = \frac{y}{t ^{2} + 81}

y = e^{\int \frac{1 - 9 t ( t ^{2} + 81 )}{e ^{t} ( t ^{2} + 81 )} d t}

Schritte zur Lösung

9 t y + e^{t} y^{'} (t) = \frac{y}{t ^{2} + 81}

Solve separable ODE:

y = e^{\int \frac{1 - 9 t ( t ^{2} + 81 )}{e ^{t} ( t ^{2} + 81 )} d t}

y = e^{\int \frac{1 - 9 t ( t ^{2} + 81 )}{e ^{t} ( t ^{2} + 81 )} d t}

x^{^{'}} - e^{t} x = 5 e^{t}

y^{^{'}} + 2 x y = x, y (0) = \frac{1}{2} + \frac{1}{2} e^{- x^{2}}

y d y = x^{2} d x

\frac{d y}{d t} = \frac{5 t ^{2}}{6 y}

\frac{d y}{y} - 5 x d x = 0