" 4."quad y^(2)+(x-(1)/(y))*(dy)/(dx)=0

Solve: y^2 + (x - 1/y)(dy)/(dx) = 0.

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

Solve the differential equation: (i) (1+y^(2))+(x-e^( tan ^(-1)y))(dy)/(dx)=0 (ii) x(dy)/(dx)+cos^(2)y=tan y(dy)/(dx)

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^((d^(3)y)/(dx^(3)))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)((dy)/(dx))=x+y , iv) log_(e)((dy)/(dx))=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

Solution of the equation x^(2)y - x^(3)(dy)/(dx)=y^(4)cosx , when y(0) =1 is

If y=sin^(-1)x then prove that (1-x^(2))(d^(y))/(dx^(2))-x(dy)/(dx)=0

If y=e ^((alpha +1)x) be solution of differential equation (d ^(2)y)/(dx ^(2)) -4 (dy )/(dx) +4y=0, then alpha is:

If y=e ^((alpha +1)x) be solution of differential equation (d ^(2)y)/(dx ^(2)) -4 (dy )/(dx) +4y=0, then alpha is: