5. Given a second order linear homogenous ordinary differential equation f(x,y,y

Question

5. Given a second order linear homogenous ordinary differential equation f(x,y,y,y)=0 and assuming y1 and y2 are both solutions to the differential equation, select other solution/s A) 245y1+173y2 B) f=0 is a solution C) 289y1 D) 245y1+289y2 E) 173y2 5. Given a second order linear homogenous ordinary differential equation f(x,y,y,y)=0 and assuming y1 and y2 are both solutions to the differential equation, select other solution/s A) 245y1+173y2 B) f=0 is a solution C) 289y1 D) 245y1+289y2 E) 173y2 5. Given a second order linear homogenous ordinary differential equation f(x,y,y,y)=0 and assuming y1 and y2 are both solutions to the differential equation, select other solution/s A) 245y1+173y2 B) f=0 is a solution C) 289y1 D) 245y1+289y2 E) 173y2

Explanation / Answer

Since we have a linear homogenous ode hence the principle of superposition holds for the two solutoins ie any linear combination of y1 and y2 is a solution

Hence, A) is a solution

B)

f=0 is the differential equation not the solution

C) it is a solution as a scalar multiple of y1

D) It is a solution as it is a linear combination of y1,y2

E) It is a solutoin

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