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I just want someone to verify if my answers are correct or not. Here is the question statement:

  1. Determine which of the following ODEs are linear. For each of the linear ODEs indicate which are homogenous.

My answers are to the right of each ODE.

no. equation classification
1 $xy''+x^2y'+(\sin x)y=x$ (linear-inhomogeneous)
2 $xy''+x^2y'+(\sin x)y=y$ (nonlinear)
3 $xy'+2e^xy=0$ (linear-homogeneous)
4 $y''+y'+\sin y=0$ (nonlinear)
5 $y''+y'+\sin x=0$ (linear-inhomogeneous)
6 $y'''+y''+x^2y'+x^3y=0$ (linear-homogeneous)
7 $y''+x^2y'+(\sin x)y=y^2$ (nonlinear)
8 $yy'+y'+2y=x$ (nonlinear)
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5
  • 1
    $\begingroup$ Seems correct to me. $\endgroup$
    – Ishan Deo
    Commented Jan 17, 2021 at 17:12
  • 2
    $\begingroup$ Why the second ode is nonlinear? $\endgroup$
    – Wang
    Commented Jan 17, 2021 at 17:12
  • 1
    $\begingroup$ Not correct. The second one is linear. Also in the future use \sin. $\endgroup$
    – K.defaoite
    Commented Jan 17, 2021 at 17:14
  • 1
    $\begingroup$ @Wang I see the second one is linear homogeneous if I rewrite the equation. Thanks. $\endgroup$ Commented Jan 17, 2021 at 17:15
  • $\begingroup$ @K.defaoite Okay, will do. $\endgroup$ Commented Jan 17, 2021 at 17:16

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