Home
Class 12
MATHS
Find the general solutions of the follow...

Find the general solutions of the following differential equations.
(i) `sin^(-1)((dy)/(dx)) = x+y`
(ii) `(dy)/(dx) = tan^(2) (x+y)`
(iii) `(dy)/(dx) = sqrt(y-x)` (iv) `(dy)/(dx) = (x-y)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
(i) Tan(x+y) - sec(x+y) = x+c
(ii) sin(2x + 2y) = 2x - 2y +c
(iii) `2sqrt(y-x)+2log (sqrt(y-x-1)) = x+c`
(iv) `(x-y+1) = c(1-x+y)e^(2x)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Excerise - 4.3 (Very Short Answer Questions)|2 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Excerise - 4.3 (Short Answer Questions)|10 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Exercise - 4.2 (Very Short Answer Questions)|3 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

  • ELLIPSE

    AAKASH SERIES|Exercise PRACTICE EXERCISE|65 Videos

Similar Questions

Explore conceptually related problems

Solve the following differential equations. sin^(-1)((dy)/(dx))=x+y

Find the general solutions of the following differential equations. (dy)/(dx) = (4x+9y +1)^(2)

Find the general solution the following differential equations xy^(2)dy = (x^(3) + y^(3))dx

Find the general solutions of the following differential equations. (i) (dy)/(dx) = e^(x+y) (ii) (dy)/(dx) = e^(y-x) (iii) (dy)/(dx) = (xy+y)/(yx+x) (iv) y(1+x)dx+x(1+y)dy = 0

Find the general solutions of the following differential equations. (i) (xy^(2) +x)dx+(yx^(2)+y)dy = 0 (ii) (dy)/(dx) = (y^(2)+2y)/(x-1) (iii) (e^(x) +1)ydx + (y+1)dx = 0

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