Engineering Board Exam Reviewer · Linear First-Order Differential Equations · easy

Determine if dy/dx+y2=x is a linear differential equation.

1. No, it is nonlinear (due to y2)
2. Yes, it is linear
3. Yes, but only for x>0
4. No, because of the x term

Answer

A. No, it is nonlinear (due to y2)

Solution

It is not linear because of the y2 term; a linear DE must have the dependent variable and its derivatives appear only to the first power.

More Linear First-Order Differential Equations questions

1. Solve the linear differential equation dy/dx+y=ex.
2. Find the integrating factor for the linear differential equation dy/dx+2/xy=x3.
3. Solve dy/dx+3y=6, given y(0)=1.
4. Find the integrating factor for dy/dx-1/xy=x2.
5. Solve xdy/dx+y=x2 for x>0.

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