一阶齐次线性微分方程的通解公式证明
举例说明：(x-2)*dy/dx=y 2*(x-2)^3 解： ∵(x-2)*dy/dx=y 2*(x-2)³ (x-2)dy=[y 2*(x-2)³]dx (x-2)dy-ydx=2*(x-2)³dx [(x-2)dy-ydx]/(x-2)²=2*(x-2)dx d[y/(x-2)]=d[(x-2)²] y/(x-2)=(x-2)² C (C是积分常数) y=(x-2)³ C(x-2) ∴原方程的通解是y=(x-2)³ C(x-2)(C是积分常数)...
举例说明：(x-2)*dy/dx=y 2*(x-2)^3 解： ∵(x-2)*dy/dx=y 2*(x-2)³ (x-2)dy=[y 2*(x-2)³]dx (x-2)dy-ydx=2*(x-2)³dx [(x-2)dy-ydx]/(x-2)²=2*(x-2)dx d[y/(x-2)]=d[(x-2)²] y/(x-2)=(x-2)² C (C是积分常数) y=(x-2)³ C(x-2) ∴原方程的通解是y=(x-2)³ C(x-2)(C是积分常数)...