Solving a Linear Differential Equation: y'''+3yy''+2y'=3x+1

[blackblanx]

Is the following a linear differential equation? I think it is since the y near the y''.


y'''+3yy''+2y'=3x+1

 

[Studiot]

No y is a solution of the equation.

The general ordinary linear diff =ion is

$${a_0}(x)\frac{{{d^n}y}}{{d{x^n}}} + {a_1}(x)\frac{{{d^{n - 1}}y}}{{d{x^{n - 1}}}} + {a_2}(x)\frac{{{d^{n - 2}}y}}{{d{x^{n - 2}}}}... + {a_n}(x)y = f(x)$$

You can have a y on the LHS only as shown

 

[blackblanx]

oh ok thank you