y^{''}+y=xcos^3(x)

解

y^{^{''}} + y = x cos^{3} (x)

y = c_{1} cos (x) + c_{2} sin (x) + \frac{24 x ^{2} sin ( x ) + 32 x cos ^{5} ( x ) - 12 x cos ( x ) - 12 x sin ( x ) sin ( 4 x ) + 128 x cos ^{3} ( x ) sin ^{2} ( x ) + 3 cos ( x ) sin ( 4 x ) - 3 sin ( x ) cos ( 4 x )}{128}

解答ステップ

y^{''} (x) + y = x cos^{3} (x)

線形 ODE を解く:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{24 x ^{2} sin ( x ) + 32 x cos ^{5} ( x ) - 12 x cos ( x ) - 12 x sin ( x ) sin ( 4 x ) + 128 x cos ^{3} ( x ) sin ^{2} ( x ) + 3 cos ( x ) sin ( 4 x ) - 3 sin ( x ) cos ( 4 x )}{128}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{24 x ^{2} sin ( x ) + 32 x cos ^{5} ( x ) - 12 x cos ( x ) - 12 x sin ( x ) sin ( 4 x ) + 128 x cos ^{3} ( x ) sin ^{2} ( x ) + 3 cos ( x ) sin ( 4 x ) - 3 sin ( x ) cos ( 4 x )}{128}