Choose the correct matching: (P) (a_{1} frac{d^{2} y}{d x^{2}}+a_{2} y frac{d y}{d x}+a_{3} y=a_{4}) (Q) (a_{1} frac{d^{3}

Question:

Choose the correct matching:

(P) $a_{1} \frac{d^{2} y}{d x^{2}}+a_{2} y \frac{d y}{d x}+a_{3} y=a_{4}$

(Q) $a_{1} \frac{d^{3} y}{d x^{3}}+a_{2} y=a_{3}$

(R) $a_{1} \frac{d^{2} y}{d x^{2}}+a_{2} x \frac{d y}{d x}+a_{3} x^{2} y=0$

(1) Non-linear differential equation

(2) Linear differential equation with constant coefficient

(3) Linear homogeneous differential equation

(4) Non-linear homogeneous differential equation

(5) Non-linear first order differential equation.
(a) P-1, Q-2, R-4
(b) P-1, Q-5, R-2
(c) P-2, Q-1, R-4
(d) P-5, Q-2, R-1.