y^'+y=cos(t),y(0)=1

Lösung

y^{^{'}} + y = cos (t), y (0) = 1

y = \frac{sin ( t )}{2} + \frac{cos ( t )}{2} + \frac{1}{2 e ^{t}}

Schritte zur Lösung

y^{'} (t) + y = cos (t)

Solve linear ODE:

y = \frac{sin ( t )}{2} + \frac{cos ( t )}{2} + \frac{1}{2 e ^{t}}

y = \frac{sin ( t )}{2} + \frac{cos ( t )}{2} + \frac{1}{2 e ^{t}}

d er i v a t i v e y = lo g_{e} (lo g_{e} (x))

h \to 0 lim (\frac{( h + 2 ) ^{3} - 8}{h})

\int \frac{1}{y} d y

\int_{0}^{1} 5 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

d er i v a t i v e (\frac{8 x + 5}{8 x - 5})^{\frac{1}{2}}