x^3y^'+2x^2y=4cos(4x)y^{-1/2}

解

x^{3} y^{^{'}} + 2 x^{2} y = 4 cos (4 x) y^{- \frac{1}{2}}

y = \frac{( 9 sin ^{2} ( 4 x ) + 4 ( 3 c _{1} sin ( 4 x ) + c _{1}^{2} ) ) ^{\frac{1}{3}}}{4 ^{\frac{1}{3}} x ^{2}}

解答ステップ

x^{3} y^{'} (x) + 2 x^{2} y = 4 cos (4 x) y^{- \frac{1}{2}}

ベルヌーイ ODE を解く:

y = \frac{( 9 sin ^{2} ( 4 x ) + 4 ( 3 c _{1} sin ( 4 x ) + c _{1}^{2} ) ) ^{\frac{1}{3}}}{4 ^{\frac{1}{3}} x ^{2}}

y = \frac{( 9 sin ^{2} ( 4 x ) + 4 ( 3 c _{1} sin ( 4 x ) + c _{1}^{2} ) ) ^{\frac{1}{3}}}{4 ^{\frac{1}{3}} x ^{2}}