d^2y/dx^2+a^2y-b^2=0求解==d^2y/dx^2+a^2y-b^2=0求解==

Question

d^2y/dx^2+a^2y-b^2=0 求解=_=
d^2y/dx^2+a^2y-b^2=0
求解=_=

Answer 1

y"+a^2*y=b^2
二阶常系数齐次线性微分方
根据特征值法则
r^2+a^2=0
r1=ai ; r2=-ai
所以 y=e^(0x)(C1*cosax+C2*sinax)+b^2=C1*cosax+C2*sinax+b^2