2x^2y+3xy^'-15y=0

Lösung

2 x^{2} y + 3 x y^{^{'}} - 15 y = 0

y = e^{- \frac{1}{3} x^{2} + c_{1}} x^{5}

Schritte zur Lösung

2 x^{2} y + 3 x y^{'} (x) - 15 y = 0

Solve separable ODE:

y = e^{- \frac{1}{3} x^{2} + c_{1}} x^{5}

y = e^{- \frac{1}{3} x^{2} + c_{1}} x^{5}

- 5 \frac{d y}{d x} = 2 y - 150

(ln (y))^{2} \frac{d y}{d x} = x^{2} y

y^{^{'}} + \frac{3}{x} y = \frac{1}{x}

8 t y + e^{t} y^{^{'}} = \frac{y}{t ^{2} + 64}

y y^{^{'}} - 4 y^{^{'}} - 5 y = 125