(dy)/(dx)y=2x^4sin(3x)

Lösung

\frac{d y}{d x} y = 2 x^{4} sin (3 x)

y = 4 (- \frac{1}{3} x^{4} cos (3 x) + \frac{4}{81} (9 x^{3} sin (3 x) + 9 x^{2} cos (3 x) - 6 x sin (3 x) - 2 cos (3 x))) + c_{1}, y = - 4 (- \frac{1}{3} x^{4} cos (3 x) + \frac{4}{81} (9 x^{3} sin (3 x) + 9 x^{2} cos (3 x) - 6 x sin (3 x) - 2 cos (3 x))) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} y = 2 x^{4} sin (3 x)

Solve separable ODE:

y = 4 (- \frac{1}{3} x^{4} cos (3 x) + \frac{4}{81} (9 x^{3} sin (3 x) + 9 x^{2} cos (3 x) - 6 x sin (3 x) - 2 cos (3 x))) + c_{1}, y = - 4 (- \frac{1}{3} x^{4} cos (3 x) + \frac{4}{81} (9 x^{3} sin (3 x) + 9 x^{2} cos (3 x) - 6 x sin (3 x) - 2 cos (3 x))) + c_{1}

y = 4 (- \frac{1}{3} x^{4} cos (3 x) + \frac{4}{81} (9 x^{3} sin (3 x) + 9 x^{2} cos (3 x) - 6 x sin (3 x) - 2 cos (3 x))) + c_{1}, y = - 4 (- \frac{1}{3} x^{4} cos (3 x) + \frac{4}{81} (9 x^{3} sin (3 x) + 9 x^{2} cos (3 x) - 6 x sin (3 x) - 2 cos (3 x))) + c_{1}

y^{2} y^{^{'}} = x^{2} - 3

y^{^{'}} + \frac{y}{5} = y^{- 3}

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

2 y y^{^{'}} = x e^{x}

y^{^{'}} = x e^{5 x - 3 y}, y (0) = 2