Find the general solution of the differential equationy′=x−y+3x−y

Painevg

Painevg

Answered

2022-01-19

Find the general solution of the differential equation
y=xy+3xy

Answer & Explanation

Terry Ray

Terry Ray

Expert

2022-01-19Added 50 answers

A differential equation is an equation in x,y and derivatives of y. A first order differential equation is on in which the highest order derivative present in the differential equation is first order.
A differential equation in some cases can be simplified to a simpler differential equation with an appropriate substitution. For given differential equation find an appropriate substitution to simplify the differential equation.
Given differential equation is y=xy+3xy. Use the substitution x-y=u. Differentiating this gives 1dydx=dudx. This can be rewritten as 1dudx=dydx. Substitute this in the differential equation and integrate.
1dudx=u+3u
1dudx=1+3u
dudx=3u
udu=3dx
u22=3x+C
u2=6x2C
u=6x2C
xy=6x2C
y=x6x2C
Hence, general solution to the differential equation is y=x6x2C

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