How Three Functions of Wroian are used to Find the

Susan Munoz

Susan Munoz

Answered question

2021-11-22

How Three Functions of Wro
ian are used to Find the Homogeneous Linear Differential Equation Whose Solution Space is Spanned by Two Given Functions?

Answer & Explanation

Prioned

Prioned

Beginner2021-11-23Added 11 answers

Step1
Let's consider two function y;(x) and y,(x) are the linearly independent solution of
yp(x)y+q(x)y=0
Let y(x) is the general solution of this equation.
Thus, y(x)=C1y1(x)+C2y2(x), where C1 and C2,are constants.
Step 2
Now by calculating the Wro
ian
W[y1,y2,y]=0
W[y1,y2,y]=y"+p(x)y+q(x)y
Where,
p(x)=W(x)W(x)
q(x)=W(y1,y2)W(y1,y2)

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