Solve the differential equation. y=x[p+√1+p²

1.	Solve the differential equation. y=x[p+√1+p²
Answer» SOLUTION <P> TO SOLVE The differential equation $\sf{y = xp + \sqrt{1 + {p}^{2} } }$ EVALUATION Here the given differential equation is $\sf{y = xp + \sqrt{1 + {p}^{2} } }$ This equation is of the form $\sf{y = xp + f(p) }$ Which is Clairaut's equation Now for Clairaut's equation the general solution is obtained replacing p by C Hence the required solution is $\sf{y = cx+ \sqrt{1 + {c}^{2} } }$ Where C is constant ━━━━━━━━━━━━━━━━ Learn more from Brainly :- 1. M+N(dy/dx)=0 where M and N are function of (A) x only (B) y only (C) constant (D) all of these brainly.in/question/38173299 2. This type of equation is of the form dy/dx=f1(x,y)/f2(x,y) (A) VARIABLE seprable (B) HOMOGENEOUS (C) exact (D) none ... brainly.in/question/38173619

Answer»