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Beliebt Rechnen >

y^'=-(2x)/((1+x^2))y+1/(x(1+x^2))

Lösung

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

Lösung

y = \frac{ln ( x )}{1 + x ^{2}} + \frac{c _{1}}{1 + x ^{2}}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{ln ( x )}{1 + x ^{2}} + \frac{c _{1}}{1 + x ^{2}}

y = \frac{ln ( x )}{1 + x ^{2}} + \frac{c _{1}}{1 + x ^{2}}

Graph

Beliebte Beispiele

integral from-1 to 1 of x^2-x-1

\int_{- 1}^{1} x^{2} - x - 1 d x

(\frac{4}{3})^{^{'}}

derivative of ln(5x^2+3y^2)

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

(1 + e^{2 x})^{^{'}}

d/(dy)(y^3+xy^2+y)

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