Home
Class 12
MATHS
Solve the following differential equatio...

Solve the following differential equations: `(dy)/(dx)=1+x+y+x y` (ii) `y-x(dy)/(dx)=a(y^2+(dy)/(dx))`

Text Solution

Verified by Experts

The correct Answer is:
`y/(1-ay)=c(a+y)`
`y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))`
or `int(dx)/(a+x)=int(dy)/(y-ay^(2))=int(1/y+a/(1-ay))dy` [By partial fractions]
Integrating we get
`log(a+x)+logc=logy-log(1-ay)`
Which is arbitary positive constant.
Thus, the solution can be written as `y/(1-ay)=c(a+x)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Solve the following differential equations: dy/dx=e^(x+y)+x^2 e^y

(dy)/(dx)=x+y

Find the order and degree, if defined, of each of the following differential equations: (i) (dy)/(dx) - cos x = 0 (ii) xy (d^(2)y)/(dx^(2)) + x((dy)/(dx))^(2) - y (dy)/(dx) = 0 (iii) y''' + y^(2) + e^(y)' = 0

Solve the differential equation : (dy)/(dx)-y/x=2x^2

Solve the following differential equations : dy/dx+sqrt((1-y^2)/(1-x^2))=0

(dy)/(dx)=(y-x)/(x+y)

Solve the following differential equations : x(1+y^2)dx+y(1+x^2)dy=0,at, x=0,y=1

Solve the differential equation (x)dy = ( 1 + y^(2))dx .

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

Solve: (dy)/(dx) = 1-x+y-xy