The order of the differential equation whose general solution is given by y= (C₁+C₂ ) (x+C₃ )-C₄ e^ x+C₅ where, C₁, C₂, C₃, C₄, C₅ are arbitrary constants, is

Step-by-step solution

We have, aligned y & = (C₁+C₂ ) (x+C₃ )-C₄ e^ x+C₅ ...(i) y & = (C₁+C₂ ) (x+C₃ )-C₄ e^x e^ C₅ aligned Now, let C₁+C₂=A, C₃=B, C₄ e^ C₅ =C y=A (x+B)-C e^x ...(ii) On differentiating w.r.t. x , we get d y d x =-A (x+B)-C e^x ...(iii) Again, differentiating w.r.t. x , we get array ll & d^2 y d x^2 =-A (x+B)-C e^x ...(iv) & d^2 y d x^2 =-y-2 C e^x & d^2 y d x^2 +y=-2 C e^x ...(v) array Again, differentiating w.r.t. x , we get d^3 y d x^3 + d y d x =-2 C e^x ...(vi) d^3 y d x^3 + d y d x = d^2 y d x^2 +y[ from Eq. (v) ]