hi i have a problem for this Differential Equations : $$ \frac{d^{3}y}{dx^3} - 9\frac{dy}{dx} = 10 - 4x $$ i know first we must solve the homogeneous equation: and my result is : $C_1 + C_2e^{3x} + C_3e^{-3x}$
i'm really confused to find yp from $10 - 4x$,
my friend said it must : $(ax+b)x$
my question is :
1. why it's not $c - (ax + b)$,
2. if it same with $c1$ from yh(homogeneous solution ) why we not multiply $c$ with x?
so $yp = cx - (ax + b) $
3. and why $(ax+b)$ must be multiplied with $x$??
can someone explain me? thanks for anyone helped me.