Consider the differential equation Verify that y1 = x is
Chapter , Problem 34RP(choose chapter or problem)
Consider the differential equation
\(x^{2} y^{\prime \prime}-\left(x^{2}+2 x\right) y^{\prime}+(x+2) y=x^{3}\).
Verify that \(y_{1}=x\) is one solution of the associated homogeneous equation. Then show that the method of reduction of order discussed in Section 4.2 leads to a second solution \(y_{2}\) of the homogeneous equation as well as a particular solution \(y_{p}\) of the nonhomogeneous equation. Form the general solution of the DE on the interval (0, ).
Text Transcription:
x^2y^prime\prime-(x^2+2x)y^prime+(x+2)y=x^3
y_1=x
y_2
y_p
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