7x^2y^'=y^'+9xe-y

解

7 x^{2} y^{^{'}} = y^{^{'}} + 9 x e - y

y = e^{\frac{l n ( 7 x + 1 ) - l n ( 7 x - 1 )}{2 7}} \cdot \int \frac{9 e x ( ( 7 x - 1 ) ^{1 - 27} ) ^{\frac{1}{2 7}}}{( 7 x + 1 ) ^{\frac{1 + 2 7}{2 7}}} d x

解答ステップ

7 x^{2} y^{'} (x) = y^{'} (x) + 9 x e - y

線形 ODE を解く:

y = e^{\frac{l n ( 7 x + 1 ) - l n ( 7 x - 1 )}{2 7}} \cdot \int \frac{9 e x ( ( 7 x - 1 ) ^{1 - 27} ) ^{\frac{1}{2 7}}}{( 7 x + 1 ) ^{\frac{1 + 2 7}{2 7}}} d x

y = e^{\frac{l n ( 7 x + 1 ) - l n ( 7 x - 1 )}{2 7}} \cdot \int \frac{9 e x ( ( 7 x - 1 ) ^{1 - 27} ) ^{\frac{1}{2 7}}}{( 7 x + 1 ) ^{\frac{1 + 2 7}{2 7}}} d x