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C) The dependent variable y is missing in the given differential equation. Solve the equation by using the substitution u = y'. y"= 1+ (y')?

C) The dependent variable y is missing in the given differential equation. Solve the equation by using the substitution u = y'. y"= 1+ (y')?

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The problem presents a differential equation where the dependent variable \( y \) is missing. The task is to solve the equation by using the substitution \( u = y' \). The differential equation provided is: \[ y'' = 1 + (y')^2 \] To solve the equation, use the substitution \( u = y' \), where \( y' \) is the first derivative of \( y \) with respect to the independent variable. Once the substitution is applied, you can explore solving the differential equation with respect to \( u \).
Transcribed Image Text:The problem presents a differential equation where the dependent variable \( y \) is missing. The task is to solve the equation by using the substitution \( u = y' \). The differential equation provided is: \[ y'' = 1 + (y')^2 \] To solve the equation, use the substitution \( u = y' \), where \( y' \) is the first derivative of \( y \) with respect to the independent variable. Once the substitution is applied, you can explore solving the differential equation with respect to \( u \).
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