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

Lösung

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

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

d er i v a t i v e sin (4 t)

d er i v a t i v e 5^{- x}

\int \frac{38}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (\frac{( a x + b y )}{( c x + d y )})

d er i v a t i v e \frac{( 3 x + 5 ) ( 2 x - 7 )}{8 x ^{2} - 3}