(d^2-3d+2)y=3sin^2(x)

Lösung

(d^{2} - 3 d + 2) y = 3 sin^{2} (x)

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

Schritte zur Lösung

(d^{2} - 3 d + 2) y = 3 sin^{2} (x)

Solve linear ODE:

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

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

(d^{2} + 3 d + 2) y = 4 cos^{2} (x)

y^{^{''}} + 3 y^{^{'}} = - 48 x^{2} e^{3} x

(d^{3} - d^{2} - d + 1) y = 1 + x^{2}

(d^{3} + 4 d) y = 4 cot (2 x)

d (x) = 243 e^{- 0} 0.1 x