Reduction of Order Problem for Differential Equations Class

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The discussion centers on a second-order linear differential equation that was initially not in standard form. The poster realized that by dividing the equation by 4, it could be transformed into the correct standard form. This adjustment allowed for the proper application of solution techniques. The importance of ensuring equations are in standard form before solving is emphasized. Correctly formatting the equation is crucial for obtaining accurate solutions in differential equations.
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Homework Statement
Find second solution for differential equation using reduction of order (see first image)
Relevant Equations
equation labeled (5) in first image in addition to equation 1
Problem statement:
1633375237245.png

Second order linear differential equation in standard from
1633375439303.png

Reasoning:
1633376079966.jpeg
 

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I just looked back at the original problem, and I realized that I did not put the equation into standard form. If I divide the equation by 4 and repeat the same process I get the correct answer.
 

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