# Classification of Linear and Nonlinear ODEs

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)
• Seems correct to me. Commented Jan 17, 2021 at 17:12
• Why the second ode is nonlinear?
– Wang
Commented Jan 17, 2021 at 17:12
• Not correct. The second one is linear. Also in the future use \sin. Commented Jan 17, 2021 at 17:14
• @Wang I see the second one is linear homogeneous if I rewrite the equation. Thanks. Commented Jan 17, 2021 at 17:15
• @K.defaoite Okay, will do. Commented Jan 17, 2021 at 17:16