Give the correct answer and solve the given equation xy′′ − y′ = (3 + x)x^{2}e^{x}

sjeikdom0 2021-01-08 Answered
Give the correct answer and solve the given equation xyy=(3+x)x2ex
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Expert Answer

krolaniaN
Answered 2021-01-09 Author has 86 answers

Given: consider the differential equation
xy"y=(3+x)x2ex
xyyx2=(3+x)ex
d(yx)=(2+x)exdx
d(yx)=(3+x)exdx+C
C is the integrating constant
yx=3ex+xexex+
y=2xex+x62ex+Cx
dydx=2xex+x2ex+Cx
dy=2xexdx+x2exdx+Cxdx+C2
C2 is the integrating constant
y=2(xexex)+x2ex2xex+xe6x+Cx22+C2
y=x2ex+X1x2+c2
Where c1=C2 is the integrating constant
Finally result:
y=x2ex+X1x2+c2

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