Use the Wronskian to determine if the given functions are linearly independent on the indicated interval.   ​f(x)=13​, ​g(x)=3x​, ​h(x)=x^2​; the real line   Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.   ​(Simplify your​ answer.)   A.The Wronskian​ W(f, g,​h)=___?. As W is identically 0 on the real line​ f(x), g(x) and​ h(x) are linearly independent.   B. The Wronskian​ W(f, g,​h)=___? As W is never 0 on the real line​ f(x), g(x) and​ h(x) are linearly independent.   C.The Wronskian​ W(f, g,​h)=___? As W is identically 0 on the real line​ f(x), g(x) and​ h(x) are linearly dependent.   D. The Wronskian​ W(f, g,​h)=___?.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use the Wronskian to determine if the given functions are linearly independent on the indicated interval.
 
​f(x)=13​, ​g(x)=3x​, ​h(x)=x^2​; the real line
 
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
 
​(Simplify your​ answer.)
 
A.The Wronskian​ W(f, g,​h)=___?. As W is identically 0 on the real line​ f(x), g(x) and​ h(x) are linearly independent.
 
B. The Wronskian​ W(f, g,​h)=___? As W is never 0 on the real line​ f(x), g(x) and​ h(x) are linearly independent.
 
C.The Wronskian​ W(f, g,​h)=___? As W is identically 0 on the real line​ f(x), g(x) and​ h(x) are linearly dependent.
 
D. The Wronskian​ W(f, g,​h)=___?. As W is never 0 on the real line​ f(x), g(x) and​ h(x) are linearly dependent.
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