Manipal MET2018MathematicsDifferential Equations
By eliminating the arbitrary constants A and B from y=A x^2+B x , we get the differential equation
Options
- Ad^3 y d x^3 =0
- Bx^2 d^2 y d x^2 -2 x d y d x +2 y=0
- Cd^2 y d x^2 =0
- Dx^2 d^2 y d x^2 +y=0
Correct answer
B. x^2 d^2 y d x^2 -2 x d y d x +2 y=0
Step-by-step solution
Given, y=A x^2+B x ....(i) On differentiating, we get array rlrl & d y d x & =2 A x+B & & d^2 y d x^2 & =2 A array d y d x - d^2 y d x^2 x=B From Eq. (i), array ll & y= 1 2 d^2 y d x^2 x^2+x [ d y d x - d^2 y d x^2 x ] & y=- 1 2 x^2 d^2 y d x^2 +x d y d x & x^2 d^2 y d x^2 -2 x d y d x +2 y=0 array