2x^2y^'=y^'+6xe-y

Lösung

2 x^{2} y^{^{'}} = y^{^{'}} + 6 x e - y

y = e^{\frac{l n ( 2 x + 1 ) - l n ( 2 x - 1 )}{2 2}} \cdot \int \frac{6 e x ( ( 2 x - 1 ) ^{1 - 22} ) ^{\frac{1}{2 2}}}{( 2 x + 1 ) ^{\frac{1 + 2 2}{2 2}}} d x

Schritte zur Lösung

2 x^{2} y^{'} (x) = y^{'} (x) + 6 x e - y

Solve linear ODE:

y = e^{\frac{l n ( 2 x + 1 ) - l n ( 2 x - 1 )}{2 2}} \cdot \int \frac{6 e x ( ( 2 x - 1 ) ^{1 - 22} ) ^{\frac{1}{2 2}}}{( 2 x + 1 ) ^{\frac{1 + 2 2}{2 2}}} d x

y = e^{\frac{l n ( 2 x + 1 ) - l n ( 2 x - 1 )}{2 2}} \cdot \int \frac{6 e x ( ( 2 x - 1 ) ^{1 - 22} ) ^{\frac{1}{2 2}}}{( 2 x + 1 ) ^{\frac{1 + 2 2}{2 2}}} d x

x \to 0 - lim (x)

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