find the real solution of (d^2y/dx^2)^2=-100

Question

MATH PROBLEM IN D.E

 

 

Answer 1

If you have written every correctly, then as a real solution you can take any linear function

y(x)=ax+b,  a, b constant (unknown)

Indeed the solution is (you twice integrate ±10i)

y₁(x)=-5i x²+C₁x+C₂

y₂(x)=5i x²+C₁x+C₂

y(x)=y₁(x)+y₂(x)=C'₁x+C'₂ is a real solution