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AP EAMCET202316 May 2023Evening ShiftMathematicsDifferential EquationsActual

The differential equation having y=(a+b) e^ c x+d as its general solution, where a, b, c, d, are arbitrary constants, is

Options

  1. Ay^ (4) +3 y y^ (3) +6 y^ (2) y^2+y=0
  2. By ^ (3) +4 yy y ^ (2) +6 y ^2 y ^ (1) +12 y =0
  3. Cy ^ (1) - y =0
  4. Dyy ^ (2) - ( y ^ (1) )^2=0

Correct answer

D. yy ^ (2) - ( y ^ (1) )^2=0

Step-by-step solution

Given y=(a+b) e^ c x+d y^1=(a+b) e^ (x+d) aligned & y^1=c y ; y^2=c y^1 & y^2= y^ y y^1 & y y^ (2) - (y^ (1) )^2=0 aligned

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