Engineering Board Exam Reviewer · Linear First-Order Differential Equations · hard
Find the general solution of (x2+1)dy/dx+4xy=x.
- y = C≤ft(x2 + 1 )2 + 1/2
- y = Cx2 + 1 + 1/4
- y = C≤ft(x2 + 1 )2 + 1/4
- y = C ≤ft(x2 + 1 )2 + 1/4
Answer
C. y = C≤ft(x2 + 1 )2 + 1/4
Solution
Standard form: y'+4x/x2+1y=x/x2+1. The integrating factor is e2 (x2+1)=(x2+1)2, so d/dx≤ft[(x2+1)2y ]=x(x2+1). Integrating, (x2+1)2y=x4/4+x2/2+c=(x2+1)2/4+C, so y= 14+C/(x2+1)2.
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