Show that `y=x+tanx` satisfies the equation `cos^(2)x(dy^(2))/(dx^(2))+2x=2y`.

Find A and B so that y=A sin3x+B cos3x satisfies the equation (d^(2)y)/(dx^(2))+4(dy)/(dx)+3y=10cos3x

Find A and B so that y=A sin3x+B cos3x satisfies the equation (d^(2)y)/(dx^(2))+4(dy)/(dx)+3y=10cos3x

Find A and B so that y=A sin3x+b cos3x satisfies the equation (d^(2)y)/(dx^(2))+4(dy)/(dx)+3y=10cos3x

If y=x+tanx , show that cos^(2)x(d^(2)y)/(dx^(2))-2y+2x=0 .

The function y=A sin x+cos x satisfies the equation (d^(2)y)/(dx^(2))+y=B , where A, B are constants. If (dy)/(dx)=2 when x = 0, then (A,B)-=

Find A\ a n d\ B so that y=Asin3x+Bcos3x satisfies the equation (d^2y)/(dx^2)+4(dy)/(dx)+3y=10cos3x .

Verify that y=e^(m cos^(-1)x) satisfies the differential equation (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0

Solve: cos^(2)x(dy)/(dx)+y=tanx

Show that the function y = xe^(-x^(2)//2) satisfies the equation x(dy/dx)=(1-x^(2))y

Verify that y=e^(m cos^-1 x) satisfies the differential equation (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0