2xp^3-6yp^2+x^4=0 #Solvablefory L868

#solvablefory #differentialequationoffirstdegreeiny Differential equation solvable for y: Let f(x,y,p)=0 be the given differential equation....(1) If (1) cannot be resolved into two rational and linear factors and (1) is of first degree in y, then it can be solved for y. (1) can be expressed in the form y=F(x,p)...(2) Differentiation of (2) w.r.t.x. gives an equation of the form p=g(x,p,dp/dx)...(3) Since (3) is an equation in two variables p and x, it can be solved. The solution of (1) is ψ(x,y,c)....(4) If it is not possible to eliminate p from (1) and (4), the general solution of (1) is given in the form Φ(x,p,c)=0, f(x,y,p)=0 or x=f1(p,c) , y=f2(p,c). This is regarded as parametric form of the required solution where p is regarded as parameter. This method is specially useful for equations in which x is absent. The general solution of the differential equation of order n contains n arbitrary constants. Singular solution: An equation ψ(x,y)=0 is called singular solution of the differential equation F(x,y,y',...,y^n)=0 if 1. ψ(x,y)=0 is a solution of the given differential equation. 2. ψ(x,y)=0 does not contain arbitrary constant and 3. ψ(x,y)=0 is not obtained by giving particular values to arbitrary constants in the general solution. For more such videos👇    • Solvable for y   You can also find me on Instagram 🌼   / mathspulse_chinnaiahkalpana   Thank you one and all for the love and support🌹 Stay tuned to 'Maths Pulse'🌸 Have a happy learning⭐ With Love, Chinnaiah Kalpana😊 #differentialequationsoffirstorderbutnotoffirstdegree #solvablefory #math #bscmathsproblems #engineeringmaths examplesonsolvablefory #mathematics #differentialequations