Question

2
1.a)
Solve the D.E xp^2 +2yp + x = 0 for p.​

Answer 1

Answer:

Simplifying

xp2 + -2yp + x = 0

Reorder the terms:

-2py + p2x + x = 0

Solving

-2py + p2x + x = 0

Solving for variable 'p'.

The solution to this equation could not be determined.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

xp^2+2yp+x=0

p(xp+2y)=-x

xp+2y=-x/p

2y=-x/p-xp

2y=-x(1/p+p)

-2y/x=(1/p+p)

1/p(1+p^2)=-2y/x

equating 1/p and (1+p^2) to -2y/x

1/p=-2y/x

p=dy/dx

1/p=dx/dy

dx/dy=-2y/x

using variable seperable method

dy(-2y)=dx(x)

integrating on both sides we get

-y^2=x^2/2+c

x^2+2y^2=c--------(1)

(1+p^2)=-2y/x

p=dy/dx

(1+d^2y/dx)=-2y/x

d^2y/dx+2y/x=-1

It is in the form of linear differential equation

I.F=e^integration of 2/x

=e^2(logx) =x^2

soln: y.I.F=integration (q(x).I.F) dx

y.x^2=integration (-1).x^2 dx

y.x^2=-2x^3/3+c--------(2)

therefore the soln is either (1) or (2)