Menu Close

dy-dt-dx-dt-t-dy-dt-y-t-dx-dt-x-




Question Number 1030 by 123456 last updated on 20/May/15
(dy/dt)−(dx/dt)=((t(dy/dt)+y)/(t(dx/dt)+x))
dydtdxdt=tdydt+ytdxdt+x
Answered by prakash jain last updated on 21/May/15
y=k_1 t,x=k_2 t  (dy/dt)=k_1 ,(dx/dt)=k_2   k_1 −k_2 =((k_1 t+k_1 t)/(k_2 t+k_2 t))=(k_1 /k_2 )  k_1 −k_2 =(k_1 /k_2 )  k_2 ^2 −k_1 k_2 +k_1 =0  k_2 =((k_1 ±(√(k_1 ^2 −4k_1 )))/2)  k_1 ^2 −4k_1 ≥0⇒k_1 (k_1 −4)≥0⇒k_1 ≤0∨k_1 ≥4
y=k1t,x=k2tdydt=k1,dxdt=k2k1k2=k1t+k1tk2t+k2t=k1k2k1k2=k1k2k22k1k2+k1=0k2=k1±k124k12k124k10k1(k14)0k10k14

Leave a Reply

Your email address will not be published. Required fields are marked *