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Lagrange's Equation - intel minds academy

Lagrange’s Equation

If the given ODE is in the form of

y=F(p)x+f(p)(1)

then is called as Lagrange’s Equation.

Problem: Solve 

y=2pxp2

———(1)

Soln. 

F(p)=2p,f(p)=p2

then (1) is Lagrange’s equation

differentiate wrt x

y=2p+2xp2ppp=2p+p(2x2p)p=p(2x2p)x=(2x2p)p=2xp+2dxdp+2px=2

which is linear ODE

IF=e2pdp=p2

then solution is

xp2=p22dp+cxp2=23p3+c(2)

from(2)

x=23p+cp2

from (1), put x in (1)

y=2p(23p+cp2)p2y=2cp+p23

so the general solution in parametric form is

x=23p+cp2, y=2cp+p23

 

 

 

 

3 thoughts on “Lagrange’s Equation”

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  2. Vipul says:

    Good content

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