y^{''}+y=(x^2+x)sin(x)

Lösung

y^{^{''}} + y = (x^{2} + x) sin (x)

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

Schritte zur Lösung

y^{''} (x) + y = (x^{2} + x) sin (x)

Solve linear ODE:

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

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

d er i v a t i v e 3 sec (x) - 7 x

x \to 8 lim (\frac{2 + 8}{2 ( 8 )})

n = 1 \sum \infty \frac{1}{n + 2}

a re a x^{2} + y^{2} = 6, x = y^{2}, y = 0

im pl i c i t \frac{d y}{d x}, x^{3} - 3 a x y + y^{3} = 0