Show that `y=e^x(A\ cos x+Bsinx)` is the solution of the differential equation `(d^2y)/(dx^2)-2(dy)/(dx)+2y=0.`

Solution of the differential equation x((dy)/(dx))^(2)+2sqrt(xy)(dy)/(dx)+y=0 is

Show that y=a e^(2x)+b e^(-x) is a solution of the differential equation (d^2y)/(dx^2)-((dy)/(dx))-2y=0.

Show that y=acos(logx)+bsin(logx) is a solution of the differential equation x^2(d^2y)/(dx^2)+(dy)/(dx)+y=0.

Show that y=a cos(log x)+b sin(log x) is a solution of the differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0

Show that y=b e^x+c e^(2x)\ is a solution of the differential equation (d^2y)/(dx^2)-3(dy)/(dx)+2y=0.

The solution of the differential equation ((x+2y^3)dy)/(dx)=y is

Show that y=a*e^(2x)+b*e^(-x) is a solution of the differential equation (d^(2)y)/(dx^(2))-(dy)/(dx)-2y=0 .

Verify that "y"="Acos x"-"Bsinx" is solution of the differential equation (d^2y)/("dx"^2)+"y"=0

Show that \ y=A e^(B x) is as solution of the differential equation (d^2y)/(dx^2)=1/y((dy)/(dx))^2dot

The solution of differential equation (d^2y)/(dx^2)=dy/dx,y(0)=3 and y'(0)=2 :