Corresponding homogeneous differential equation
y′−x2y=0
ydy=x2dx Integrate
∫ydy=∫x2dx
y=Cx2 Then
y′=C′x2+2Cx Substitute
C′x2+2Cx−x2Cx2=−x23
C′x2=−x23
C′=−x43 Integrate
C=∫(−x43)dx
C=x31+C1 The general solution of the given differential equation is
y=x1+C1x2
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