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

Lösung

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

y = - \frac{e ^{- t (- n^{2} + 1) - c_{1} (- n^{2} + 1)}}{n ( 1 - n ^{2} )} + \frac{2 ( - 1 ) ^{n}}{n ( 1 - n ^{2} )}

Schritte zur Lösung

y^{'} (t) + (1 - n^{2}) y = \frac{2 ( - 1 ) ^{n}}{n}

Solve separable ODE:

y = - \frac{e ^{- t (- n^{2} + 1) - c_{1} (- n^{2} + 1)}}{n ( 1 - n ^{2} )} + \frac{2 ( - 1 ) ^{n}}{n ( 1 - n ^{2} )}

y = - \frac{e ^{- t (- n^{2} + 1) - c_{1} (- n^{2} + 1)}}{n ( 1 - n ^{2} )} + \frac{2 ( - 1 ) ^{n}}{n ( 1 - n ^{2} )}

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

\frac{d y}{d x} y = x^{2} - 4 x

y^{^{'}} - 3 y = 9, y (1) = 6

- y^{^{'}} - 3 y = 0

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