3y^{''}+7y^'+2y=3x^2+3x+1,y(0)=0,y^'(0)=0

Lösung

3 y^{^{''}} + 7 y^{^{'}} + 2 y = 3 x^{2} + 3 x + 1, y (0) = 0, y^{^{'}} (0) = 0

y = (- \frac{1}{10} - \frac{55}{2}) e^{- \frac{x}{3}} + \frac{1}{10} e^{- 2 x} + \frac{3 x ^{2}}{2} - 9 x + \frac{55}{2}

Schritte zur Lösung

3 y^{''} (x) + 7 y^{'} (x) + 2 y = 3 x^{2} + 3 x + 1

Solve linear ODE:

y = (- \frac{1}{10} - \frac{55}{2}) e^{- \frac{x}{3}} + \frac{1}{10} e^{- 2 x} + \frac{3 x ^{2}}{2} - 9 x + \frac{55}{2}

y = (- \frac{1}{10} - \frac{55}{2}) e^{- \frac{x}{3}} + \frac{1}{10} e^{- 2 x} + \frac{3 x ^{2}}{2} - 9 x + \frac{55}{2}

\frac{\partial}{\partial x} (x y - x - 3 y)

\int \frac{1 + sin ( x )}{1 + sin ( x ) - cos ( x )} d x

\int \frac{7}{x ^{3}} d x

d er i v a t i v e y = x^{10} e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = t^{2}