Solve the IVP xy’+3y=4x y(1)=3

The subject is Diffrential Equations

Solve the IVP xy’+3y=4x    y(1)=3
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1 Answer

Divide through by x:

y'+3y/x=4. Introduce integrating factor e∫3dx/x=e3ln(x)=x3.

x3y'+3x2y=4x3, d(x3y)=4x3,

x3y=x4+C. When x=1, y=3:

3=1+C, C=2, x3y=x4+2, or y=(x4+2)/x3.

by Top Rated User (1.2m points)

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