大一高数题求一四次多项式P(x)与f(x)=e^x一致且前四个倒数于x=0

题意就是p(x)与f(x)在x=0时相等,并且它们的一阶二阶三阶四阶导数在x=0时也相等
p(x)=ax^4+bx^3+cx^2+dx+e
p'(x)=4ax^3+3bx^2+2cx+d
p''(x)=12ax^2+6bx+2c
p'''(x)=24ax+6b
p''''(x)=24a
p(0)=f(0)=1
p'(0)=f'(0)=1
p''(0)=f''(0)=1
p'''(0)=f'''(0)=1
p''''(0)=f''''(0)=1
解方程,a=1/24,b=1/6,c=1/2,d=1,e=1
ps.e^x指以e为底以x为指数的幂