y^{''}+3y^'+y=(2-6x)cos(x)-9sin(x)

Lösung

y^{^{''}} + 3 y^{^{'}} + y = (2 - 6 x) cos (x) - 9 sin (x)

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

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) + y = (2 - 6 x) cos (x) - 9 sin (x)

Solve linear ODE:

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

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

d er i v a t i v e g (x) = \frac{7}{4} x^{2} - 3 x + 12

\int \frac{y}{y ^{2} + 1} d y

\int \frac{4 x}{4 x ^{2} + 2 y ^{2}} d x

\int \frac{( u )}{( u + 1 ) ( u - 1 )} d u

\frac{d}{d x} (e^{3 x^{3} - x})