Engineering Board Exam Reviewer · Linear First-Order Differential Equations · medium
Find the general solution of xdy/dx+2y=x2 for x>0.
- y = Cx2 + x24
- y = Cx2 + x22
- y = C x2 + x24
- y = Cx2 + x33
Answer
A. y = Cx2 + x24
Solution
Standard form: y'+ 2xy=x. The integrating factor is x2: d/dx(x2y)=x3 x2y=x4/4+C y=x2/4+C/x2.
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