4y^{''}+2y=4x^3+5x^2-x+7

Lösung

4 y^{^{''}} + 2 y = 4 x^{3} + 5 x^{2} - x + 7

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 2 x^{3} + \frac{5 x ^{2}}{2} - \frac{49 x}{2} - \frac{13}{2}

Schritte zur Lösung

4 y^{''} (x) + 2 y = 4 x^{3} + 5 x^{2} - x + 7

Solve linear ODE:

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 2 x^{3} + \frac{5 x ^{2}}{2} - \frac{49 x}{2} - \frac{13}{2}

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 2 x^{3} + \frac{5 x ^{2}}{2} - \frac{49 x}{2} - \frac{13}{2}

y^{^{''}} - 3 y^{^{'}} + 2 y = cos (x), y^{^{'}} (0) = 2, y (0) = 0

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

y^{^{''}} + 4 y = t^{2} + 4 e^{t}, y (0) = 0, y^{^{'}} (0) = 3

y^{^{''}} - 4 y = 4 sin (2 x)

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