# Question help please I need number 4 using Ricatti equation ; { Problems: Solve dy 4 dy 1. =-2-y + y2; y = 2.2 dx dy 3. = 2x + (1 + 2e*) y + y2; y = -et. dx sec? x - (tan x) y + y2; yı = tan x. dx dy today wi susied 1. The Equation of Alcal The Alcetti equation is nonlinear equation dx = P(x) + Q(x)y + R(x)y?. named after an llalian mathematician-philosopher Count Macobo Francesco Ricard 11676 – 1754). In many cases, depends on P(x), Q(x) and R(r), the solution of Eq. (1) cannot be expressed in terms of elementary function (an elementary function is a function of a single variable composed of particular simple functions) If y, is a known particu ar solution of the Ricatti equation, show that a family of solutions of Eq. (1) is v= v1 + 1 where w is the solution of

RR3M5E The Asker · Advanced Mathematics
help please I need number 4 using Ricatti equation
Transcribed Image Text: ; { Problems: Solve dy 4 dy 1. =-2-y + y2; y = 2.2 dx dy 3. = 2x + (1 + 2e*) y + y2; y = -et. dx sec? x - (tan x) y + y2; yı = tan x. dx dy today wi susied 1. The Equation of Alcal The Alcetti equation is nonlinear equation dx = P(x) + Q(x)y + R(x)y?. named after an llalian mathematician-philosopher Count Macobo Francesco Ricard 11676 – 1754). In many cases, depends on P(x), Q(x) and R(r), the solution of Eq. (1) cannot be expressed in terms of elementary function (an elementary function is a function of a single variable composed of particular simple functions) If y, is a known particu ar solution of the Ricatti equation, show that a family of solutions of Eq. (1) is v= v1 + 1 where w is the solution of
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Transcribed Image Text: ; { Problems: Solve dy 4 dy 1. =-2-y + y2; y = 2.2 dx dy 3. = 2x + (1 + 2e*) y + y2; y = -et. dx sec? x - (tan x) y + y2; yı = tan x. dx dy today wi susied 1. The Equation of Alcal The Alcetti equation is nonlinear equation dx = P(x) + Q(x)y + R(x)y?. named after an llalian mathematician-philosopher Count Macobo Francesco Ricard 11676 – 1754). In many cases, depends on P(x), Q(x) and R(r), the solution of Eq. (1) cannot be expressed in terms of elementary function (an elementary function is a function of a single variable composed of particular simple functions) If y, is a known particu ar solution of the Ricatti equation, show that a family of solutions of Eq. (1) is v= v1 + 1 where w is the solution of
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5SHBIQ

(dy)/(dx)=sec^(2)x-(tan x)y+y^(2),quady_(1)=tan x.Companing it with (dy)/(dx)=P(x)+Q(x)y+R(x)y^(2) we get,P(x)=sec^(2)x,Q(x)=-tan x,quad R(x)=1.Since y_(1)=tan x is a panticulan solution let y=tan x+u then (dy)/(dx)=Sec^(2)x+(du)/(dx).multiplying (2) by I ... See the full answer