x(dy)/(dx)+2y=x^2

Lösung

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

y = \frac{x ^{2}}{4} + \frac{c _{1}}{x ^{2}}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{x ^{2}}{4} + \frac{c _{1}}{x ^{2}}

y = \frac{x ^{2}}{4} + \frac{c _{1}}{x ^{2}}

x \to 0 lim (\frac{x}{sin ^{2} ( x )})

\frac{d}{d x} (\frac{x}{8 x + 3})

\frac{d y}{d x} = (3 - 2 y) \cdot x^{3}

\int \frac{ln ( x )}{x ( 1 + ln ^{2} ( x ) )} d x

\frac{d}{d x} ((5 x^{2} - 2) (x^{3} + 3 x))