" 12."x(dy)/(dx)+2y=x^(2),x!=0

x(dy)/(dx)+y=3x^(2)-2,x>0

x(dy)/(dx)+2y-x^(2)logx=0

(dy)/(dx)+(x-2y)/(2x-y)=0

x(x-y)dy+y^(2)dx=0

x(x-y)dy+y^(2)dx=0

For each of the following differential equations verify that the accompanying functions a solution. Differential Function (a) x(dy)/(dx)=y, y=a x (b) x+y(dy)/(dx)=0, y=+-sqrt(a^2-x^2) (c) x(dy)/(dx)y=y^2, y=a/(x+a) (d) x^3(d^2y)/(dx^2)=1, y=a x+b+1/(2x) (e) y=((dy)/(dx))^2, y=1/4(x+-a)^2

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

y^2+x^2(dy)/(dx)=x y(dy)/(dx)