Reducible to Homogeneous Differential Equation

The substituting y=vx reduces the homogeneous differential equation (dy)/(dx)=(y)/(x)+tan.(y)/(x) to the form

Reducible To Linear Differential Equations

The substituion y=z^(alpha) transforms the differential equation (x^(2)y^(2)-1)dy+2xy^(3)dx=0 into a homogeneous differential equation for

Consider the differential equation (dy)/(dx)=(y^(3))/(2(xy^(2)-x^(2))) Statement 1 The substitution z=y^(2) transforms the above equation into first order homogeneous differential equation Statement 2: The solution of this differential equation is y^(2)e^((-y^(2))/(x))=C

Identify the statement(s) which is/are true. (a) f( x , y )= e^( y/ x )+tan y/ x is a homogeneous of degree zero. (b) xln y/ x dx+ y^(2)/ x *sin^-1(y/ x ) dy=0 is a homogeneous differential equation. (c)f( x ,y )= x^(2)+sinx cosy is a non homogeneous. (d)( x^(2)+ y^(2))dx-(x y^(2)-y^(3))dy=0 is a homogeneous differential equation.

Show that y^(2)dx + (xy + x^(2))dy = 0 is a homogeneous differential equation. Also find its general solution.

Homogeneous Differential Equations with Illustrations

Homogeneous Differential Equations with Illustrations

Which of the following is a homogeneous differential equation ?