Let's first solve the general solution of the corresponding homogeneous equation: DP/DX = P.

Then the variable separation method lnp=x+C 1.

So p = ce (x)

Because c is a constant, we follow the law of constant variation.

p=C(x)e^(x)

Bringing p into the original equation includes

c(x)e^(x)+c'(x)e^(x)-c(x)e^(x)=x？ →? C'(x)e^(x)=x

dC(x)=x*e^(-x)dx

c(x)=-[x*e^(-x)-∫e^(-x)dx]=-x*e^(-x)-e^(-x)+c 1

So get the result

p=(-x*e^(-x)-e^(-x)+c 1)e^(x)→？ p=-x*- 1+C 1e^(x)。

Extended data:

Constant variation method is the research result of Lagrange for eleven years, and we only use his conclusion, without process.

Introduction of Lagrange

Joseph Lagrange (1736~ 18 13) is a famous French mathematician and physicist. 17361was born in Turin, Italy on October 25th and died in Paris on April 30th, 2003. He has made historic contributions in mathematics, mechanics and astronomy, especially in mathematics.

Baidu encyclopedia-Changshu variation method