The general solution of the differential equation, `y^(prime)+yvarphi^(prime)(x)-varphi^(prime)(x) varphi(x)=0`, where `varphi(x)` is a known function, is

The solution of the differential equation y^(prime)y^(primeprimeprime)=3(y^(primeprime))^2 is

The general solution of the differential equation (y dx - x dy)/(y ) = 0 is

The general solution of the differential equation e^(x) dy + (y e^(x) + 2x)dx = 0 is

The solution to the differential equation ylogy+x y^(prime)=0, where y(1)=e , is

Find the general solution of the differential equation x (dy)/(dx) + 2y = x^(2)(x ne 0) .

The solution of the differential equation y^(prime prime prime)-8y^(prime prime)=0, where y(0)=1/8,y^(prime)(0)=0,y^(prime prime)(0)=1 , is

The solution of differential equation y y^(prime)=x((y^2)/(x^2)+(f((y^2)/(x^2)))/(f^(prime)((y^2)/(x^2)))) is

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^(primeprime)+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) P=y+x (b) P=y-x (c) P+Q=1-x+y+y^(prime)+(y^(prime))^2 (d) P-Q=x+y-y^(prime)-(y^(prime))^2

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,