x^3y^'-(8x^2-5)y=0,y(1)=2

Lösung

x^{3} y^{^{'}} - (8 x^{2} - 5) y = 0, y (1) = 2

y = 2 e^{\frac{5}{2 x ^{2}} - \frac{5}{2}} x^{8}

Schritte zur Lösung

x^{3} y^{'} (x) - (8 x^{2} - 5) y = 0

Solve separable ODE:

y = 2 e^{\frac{5}{2 x ^{2}} - \frac{5}{2}} x^{8}

y = 2 e^{\frac{5}{2 x ^{2}} - \frac{5}{2}} x^{8}

\frac{d y}{d x} = cy - 1

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

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

(x^{4} + 1) y^{^{'}} + 2 x^{3} y = x^{3}

y^{^{'}} = 2 - 3 y