Some second-order differential equations can be reduced to a first- order equation by means of a...

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Some second-order differential equations can be reduced to a first- order equation by means of a substitution. In Problems 31 and 32, use the substitution u = y' to reduce the given differential equation to a first-order equation, and then solve that equation by a method discussed in this section. Then use u = y' again to find the solution y of the given equation. y"+ (y)² = 0 y" - 2y' = 4x Some second-order differential equations can be reduced to a first- order equation by means of a substitution. In Problems 31 and 32, use the substitution u = y' to reduce the given differential equation to a first-order equation, and then solve that equation by a method discussed in this section. Then use u = y' again to find the solution y of the given equation. y"+ (y)² = 0 y" - 2y' = 4x