AP EAMCET201923 Apr 2019Morning ShiftMathematicsDifferential EquationsActual
The differential equation corresponding to the family of curves (y=e^x(A x+B x) ) is
Options
- A(y^ +y^ +y=0 )
- B(y^ +2 y^ +2 y=0 )
- C(y^ -2 y^ +2 y=0 )
- D(y^ -2 y^ -2 y=0 )
Correct answer
C. (y^ -2 y^ +2 y=0 )
Step-by-step solution
Given, curve (y=e^x(A x+B x) ) ...(i) So, (y^ =e^x(-A x+B x)+e^x(A x+B x) ) ( y^ -y=e^x(-A x+B x) ) ...(ii) So, (y^ -y^ =e^x(-A x-B x) ) (+e^x(-A x+B x) ) ( y^ -y^ =-y+y^ -y ) [from Eqs. (i) and (ii)] ( y^ -2 y^ +2 y=0 ) Hence, option (c) is correct.