A solution of differential equation is a relation between the variables (independent and dependent), which is free of derivatives of any order and satisfies the differential equation identically. Differential equation General solution (A) 2xy2dx=ex(dy−ydx) (P) 4x3y+6ex−3y3=cy(B) y(2x2y+ex)dx=(ex+y3)dy(Q) x+loge(x2+y2)=c(C) (x2+y2+2x)dx+2ydy=0(R) x2loge(x2y2)+y3=cx2(D) (2x2y−2y4)dx+(2x3+3xy3)dy=0(S) x2y+ex=cy Here, c is an integration constant. Which of the following is the CORRECT combination?

A solution of differential equation is a relation between the variable

1.	A solution of differential equation is a relation between the variables (independent and dependent), which is free of derivatives of any order and satisfies the differential equation identically. Differential equation General solution (A) 2xy2dx=ex(dy−ydx) (P) 4x3y+6ex−3y3=cy(B) y(2x2y+ex)dx=(ex+y3)dy(Q) x+loge(x2+y2)=c(C) (x2+y2+2x)dx+2ydy=0(R) x2loge(x2y2)+y3=cx2(D) (2x2y−2y4)dx+(2x3+3xy3)dy=0(S) x2y+ex=cy Here, c is an integration constant. Which of the following is the CORRECT combination?
Answer» A solution of differential equation is a relation between the variables (independent and dependent), which is free of derivatives of any order and satisfies the differential equation identically. $\begin{matrix} Differential equation & General solution (A) 2 x y^{2} d x = e^{x} (d y - y d x) & (P) 4 x^{3} y + 6 e^{x} - 3 y^{3} = c y (B) y (2 x^{2} y + e^{x}) d x = (e^{x} + y^{3}) d y & (Q) x + {log}_{e} (x^{2} + y^{2}) = c (C) (x^{2} + y^{2} + 2 x) d x + 2 y d y = 0 & (R) x^{2} {log}_{e} (x^{2} y^{2}) + y^{3} = c x^{2} (D) (2 x^{2} y - 2 y^{4}) d x + (2 x^{3} + 3 x y^{3}) d y = 0 & (S) x^{2} y + e^{x} = c y \end{matrix}$ Here, $c$ is an integration constant. Which of the following is the CORRECT combination?