`(dy)/(dx)=(3x^(2))/(1-e^(-y))`

Solve : (dy)/(dx)=e^(3x-2y)+x^(2)e^(-2y)

Solve: (dy)/(dx)=1/(sin^4x+cos^4x) (ii) (dy)/(dx)=(3e^(2x)+3e^(4x))/(e^x+e^(-x))

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) or, (dy)/(dx)+e^(y-x)=0

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1))

STATEMENT -1 : for the function y= f(x), f(x) ,({1+((dy)/dx)^(2)}^(3/2))/((d^(2)y)/(dx^(2))) = - ({1+ (dx/dy)^(2)}^(3/2))/((d^(2)x)/(dy^(2))) STATEMENT -2 : (dy)/(dx) = (1/(dx))/dy and (d^(2)y)/(dx^(2)) = d/dx (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

Integrating factor of the differential equation (x+1)(dy)/(dx)-y=e^(3x)(x+1)^(2) , is

The solution of the differential equation x=1+x y(dy)/(dx)+(x^2y^2)/(2!)((dy)/dx)^2+(x^3y^3)/(3!)((dy)/(dx))^3+... i s

Solve the equation (dy)/(dx)=1/x=(e^y)/(x^2)

If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2