Solve the differential equations (1) xy'-2y=x^3e^x (2) (2ydx+dy)e^2x=0

Aneeka Hunt 2021-02-05 Answered
Solve the differential equations
(1) xy2y=x3ex
(2) (2ydx+dy)e2x=0
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Luvottoq
Answered 2021-02-06 Author has 95 answers
(1)Here the differential equation is given by xy2y=x3ex.
This implies that y2x,y=x2ex.The integrating factor is
e2xdx=e2logx=1x2.Multiplying both side by 1x2 we get
yx22x3y=ex.
Taking integral we get
yx2=exdx+c
yx2=exdx+c
y=x2exdx+cx2,
where c is an arbitrary constant.
(2)Here the differential equation is given by (2ydx+dy)e2x=0.Now
(2ydx+dy)e2x=0
(2ydx+dy)e2x=0
dyy=2dx
dyy=2dx
logy=2x+c
y=e2x+c,
where c is an arbitrary constant.

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions