Question

4. Solve Y = x + 3 by taking it as a Clairaut equation.

Answer 1

4) и т given that yan dy + 3 .....o A Rifferential equation of the form o f Ya put +()-,,Þ=- ca. Dre --- called calairaut's equation and it's complete is primitive is c is a constant. and 1 Y= cn ++(c) , where taking © os a abainaut equation companing 0 Wirth ® we gel +()=3 So, to -3 so the complete primitive on Solution of t is Yachtt(e) o r, y = cut3 Where c is a constant get the solution in the following way differentiating 0 With respect to a we gent, we or, e 20 or, e de a constame (say e)

wsing ey hey ac in @ we get the solution of the given differential etuation as y = xxc t3 on, y=cnt3 , where o is a constant. So, the solution of the given differential equation Ta crit 3] , where is a constane