Form the differential equation, if `y^(2)=4a(x+a),` where a is arbitary constants.

Form the differential equation of y=px+(p)/(sqrt(1+p^(2).

If y_1 and y_2 are the solution of the differential equation (dy)/(dx)+P y=Q , where P and Q are functions of x alone and y_2=y_1z , then prove that z=1+cdote^(-intQ/(y_1)dx), where c is an arbitrary constant.

Statement I The order of differential equation of all conics whose centre lies at origin is , 2. Statement II The order of differential equation is same as number of arbitary unknowns in the given curve.

If the differential equation of the family of curve given by y=Ax+Be^(2x), where A and B are arbitary constants is of the form (1-2x)(d)/(dx)((dy)/(dx)+ly)+k((dy)/(dx)+ly)=0, then the ordered pair (k,l) is

Form the differential equation representing the family of curves y = a sin ( x + b) , where a, b are arbitrary constants.

If intx.e^(2x)dx=e^(2x)f(x)+c where c is arbitary constant then f(x)=…….

Solve the differential equation (dy)/(dx)=(2y-6x-4)/(y-3x+3).

Find the real value of m for which the substitution y=u^m will transform the differential equation 2x^4y(dy)/(dx)+y^4=4x^6 in to a homogeneous equation.

The differential equation having y=(sin^(-1)x)^(2)+A(cos^(-1)x)+B , where A and B are abitary constant , is

Form the differential equation of the family of circles touching the y-axis at origin.