(1+y^(2))+(x-e^(-(a-n)^(-1)))(dy)/(dx)=0quad ,quad y((7)/(2))=0

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)

(1+3e^((y)/(x)))dy+3e^((y)/(x))(1-(y)/(x))dx=0

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

(1-2e^((x)/(y)))dx-2e^((x)/(y))(1-(x)/(y))dy=0

(d^(2)y)/(dx^(2))=(1)/(1+x^(2)) whenx =0,y=0 and (dy)/(dx)=0

(1+e^((x)/(y)))dx+e^((x)/(y))(1-(x)/(y))dy=0

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

(1+3e^((y)/(x)))dy+3e^((y)/(x))(1-(y)/(x))dx=0 , given that y=0 and x=1