Answer to Question #327696 in Mechanics | Relativity for John

Question #327696

3d^2y/dx^2+dy/dx-14y=0 ; y=(0) ,y'=(0)=-1


1
Expert's answer
2022-04-12T16:12:42-0400

3y+y14y=0,3y''+y'-14y=0,

y=c1e7x3+c2e2x,y=c_1e^{-\frac{7x}3}+c_2e^{2x},

y(0)=0:c1=c2,y(0)=0: c_1=-c_2,

y(0)=1:c2=76c112,y'(0)=-1: c_2=\frac 76 c_1-\frac 12,

c1=313, c2=313,c_1=\frac3{13},~c_2=-\frac 3{13},

y=313e7x3313e2x.y=\frac 3{13}e^{-\frac{7x}3}-\frac 3{13}e^{2x}.


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