(t^2+25)(dy)/(dt)+2ty=t^2(t^2+25)

Lösung

(t^{2} + 25) \frac{d y}{d t} + 2 t y = t^{2} (t^{2} + 25)

y = \frac{t ^{5}}{5 ( t ^{2} + 25 )} + \frac{25 t ^{3}}{3 ( t ^{2} + 25 )} + \frac{c _{1}}{t ^{2} + 25}

Schritte zur Lösung

(t^{2} + 25) \frac{d y}{d t} + 2 t y = t^{2} (t^{2} + 25)

Solve linear ODE:

y = \frac{t ^{5}}{5 ( t ^{2} + 25 )} + \frac{25 t ^{3}}{3 ( t ^{2} + 25 )} + \frac{c _{1}}{t ^{2} + 25}

y = \frac{t ^{5}}{5 ( t ^{2} + 25 )} + \frac{25 t ^{3}}{3 ( t ^{2} + 25 )} + \frac{c _{1}}{t ^{2} + 25}

in v erse l a pl a ce \frac{( 2 s + 2.5 )}{( s + 0.5 )}

p a r i t y ln (csc (x) - cot (x))

d er i v a t i v e \frac{1}{( 2 x ^{3} + 3 x + 1 ) ^{\frac{3}{4}}}

n or ma l y = e^{2 x}, at x = ln (2)

\frac{\partial}{\partial y} (y cos (x y) + e^{x})