一阶线性微分方程
dy/dx+P(x)y=Q(x)
通解y=e^-∫P(x)dx{∫Q(x)[e^∫P(x)dx]dx+C}
代进去就可以了
y=e^-∫2xdx{2e^(-x^2)[e^∫2xdx]dx+C}
=e^(-x^2){∫2e^(-x^2)*e^(x^2)dx+C}
=e^(-x^2)[∫2dx+C]
=(2x+C)*e^(-x^2)
求道高数题的答案 求微分方程1/2y'+xy=e^(-x^2)的通解
一阶线性微分方程
dy/dx+P(x)y=Q(x)
通解y=e^-∫P(x)dx{∫Q(x)[e^∫P(x)dx]dx+C}
代进去就可以了
y=e^-∫2xdx{2e^(-x^2)[e^∫2xdx]dx+C}
=e^(-x^2){∫2e^(-x^2)*e^(x^2)dx+C}
=e^(-x^2)[∫2dx+C]
=(2x+C)*e^(-x^2)