Which of the following differential equations has `y=c_1e^x+c_2e^(-x)`as the general solution?(A) `(d^2y)/(dx^2)+y=0` (B) `(d^2y)/(dx^2)-y=0` (C) `(d^2y)/(dx^2)+1=0` (D) `(d^2y)/(dx^2)-1=0`

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

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

The general solution of the equation ((d^3y)/(dx^3)) - 7 ((d^2y)/(dx^2)) +16 (dy)/(dx) -12 y=0

If x=log pandy=(1)/(p), then (a) (d^(2)y)/(dx^(2))-2p=0 (b) (d^(2)y)/(dx^(2))+y=0 (c) (d^(2)y)/(dx^(2))+(dy)/(dx)=0( d) (d^(2)y)/(dx^(2))-(dy)/(dx)=0

y = Ae^(x) + Be^(-2x) is a solution of the D.E. (d^(2)y)/(dx^(2) )+ (dy)/(dx) -2y = 0

Show that y=a e^(2x)+b e^(-x) is a solution of the differential equation (d^2y)/(dx^2)-((dy)/(dx))-2y=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

Form the differential equation by eliminating A,B from y=e^(5x) (Ax+B) is (A) (d^(2)y)/dx^(2) +10(dy /dx) +25y=0 (B) (d^(2)y) /dx^(2) -10(dy /dx)+25y=0 (C) (d^(2)y) /dx^(2) +10(dy /dx) -25y=0 (D) (d^(2)y) /dx^(2) -10(dy /dx) -25y=0