What is expand 2uy^2(ydu+udy)+(y^2-3y^2u^2)du ?

The solution to expand 2uy^2(ydu+udy)+(y^2-3y^2u^2)du is 2uy^3du+2u^2y^2dy+y^2du-3u^2y^2du

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expand 2uy^2(ydu+udy)+(y^2-3y^2u^2)du

expand

2 u y^{2} (y d u + u d y) + (y^{2} - 3 y^{2} u^{2}) d u

2 u y^{3} d u + 2 u^{2} y^{2} d y + y^{2} d u - 3 u^{2} y^{2} d u

Solution steps

2 u y^{2} (y d u + u d y) + (y^{2} - 3 y^{2} u^{2}) d u

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

Expand

2 u y^{2} (y d u + u d y) : 2 u y^{3} d u + 2 u^{2} y^{2} d y

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

Expand

d u (y^{2} - 3 y^{2} u^{2}) : y^{2} d u - 3 u^{2} y^{2} d u

= 2 u y^{3} d u + 2 u^{2} y^{2} d y + y^{2} d u - 3 u^{2} y^{2} d u

e^{(a + ib)^{2}} e^{(a + ib)^{2}}

\frac{e ^{5 x}}{( e ^{2 x} - 1 ) ^{2}}

36 (e^{- 0.1 t} - 0.1 e^{- 0.1 t} t)

x^{2} + (x + 4) e^{- x}

\frac{sin ( 2 x )}{2 cos ^{2} ( x ) \cdot ( 1 + cos ( x ) )}

What is expand 2uy^2(ydu+udy)+(y^2-3y^2u^2)du ?
The solution to expand 2uy^2(ydu+udy)+(y^2-3y^2u^2)du is 2uy^3du+2u^2y^2dy+y^2du-3u^2y^2du