设f(x)满足f"(x)+f'(x)+f(x)=e^x+2,且f(0)=1,f'(0)=0,求f(x)

问题描述:

设f(x)满足f"(x)+f'(x)+f(x)=e^x+2,且f(0)=1,f'(0)=0,求f(x)

x=0带入得到f"(x)=2 继而f'(x)=2x+c1
f(x)=x^2+c1x+c2
然后x=0带入2个方程 c1=0 c2=1
f(x)=x^2+1