y^{''}+y=(t^2+t)sin(t)

Lösung

y^{^{''}} + y = (t^{2} + t) sin (t)

y = c_{1} cos (t) + c_{2} sin (t) - \frac{t ^{3} cos ( t )}{6} + \frac{t ^{2} sin ( t )}{4} - \frac{t ^{2} cos ( t )}{4} + \frac{t sin ( t )}{4} + \frac{t cos ( t )}{4}

Schritte zur Lösung

y^{''} (t) + y = (t^{2} + t) sin (t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) - \frac{t ^{3} cos ( t )}{6} + \frac{t ^{2} sin ( t )}{4} - \frac{t ^{2} cos ( t )}{4} + \frac{t sin ( t )}{4} + \frac{t cos ( t )}{4}

y = c_{1} cos (t) + c_{2} sin (t) - \frac{t ^{3} cos ( t )}{6} + \frac{t ^{2} sin ( t )}{4} - \frac{t ^{2} cos ( t )}{4} + \frac{t sin ( t )}{4} + \frac{t cos ( t )}{4}

im pl i c i t \frac{d y}{d x}, x y = 18

d er i v a t i v e f (t) = \frac{4 t + 8}{t + 3}

\int \frac{x}{1 + 3 x} d x

\int \frac{e ^{2 x}}{( e ^{x} + 1 ) ^{3}} d x

\int_{- π}^{π} cos^{2} (9 x) d x