Question

求一阶线性非齐次微分方程dy/dx-y=2的通解

Answer 1

问：求一阶线性非齐次微分方程dy/dx-y=2的通解

答：一阶线性非齐次微分方程dy/dx-y=2的通解:(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)