`(x^3+x^2+x+1)(dy)/(dx)=2x^2+x ; y=1w h e nx=0`

Find the particular solution of the differential equation (dy)/(dx)=-4x y^2 given that y=1,w h e nx=0.

Find the particular solution of the differential equation x(x^2-a)(dy)/(dx)=1;\ \ \ \ \ y=0\ \ "w h e n"\ x=2

Solve the differential equation x^2dy+y(x+y)dx=0, given that y=1\ w h e n\ x=1.

Solve the differential equation x^2dy+y(x+y)dx=0, given that y=1\ w h e n\ x=1.

For each of the following differential equations verify that the accompanying functions a solution. Differential Function (a) x(dy)/(dx)=y, y=a x (b) x+y(dy)/(dx)=0, y=+-sqrt(a^2-x^2) (c) x(dy)/(dx)y=y^2, y=a/(x+a) (d) x^3(d^2y)/(dx^2)=1, y=a x+b+1/(2x) (e) y=((dy)/(dx))^2, y=1/4(x+-a)^2

(dy)/(dx)=2e^(x)y^(3) , when x=0, y=(1)/(2)

Find the derivative of f(x)={(x-1)/(2x^2-7x+5)w h e nx!=1=1/3w h e nx=1a tx=1.

Find the derivative of f(x)={(x-1)/(2x^2-7x+5)w h e nx!=1 and-1/3w h e nx=1} atx=1.

Find the particular solution of the differential equation (1 + e^(2x)) dy + (1 + y^2) e^x dx = 0 , given that y = 1 w h e n x = 0 .

Find the particular solution of the differential equation ; (x^2+x y)dy=(x^2+y^2)dx given that y=0\ w h e n\ x=1.