Question Number 1030 by 123456 last updated on 20/May/15

(dy/dt)−(dx/dt)=((t(dy/dt)+y)/(t(dx/dt)+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