Solve differential equation xy'-2x^2y= e^(x^2)

floymdiT 2020-12-02 Answered
Solve differential equationxy2x2y=e(x2)
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Expert Answer

Yusuf Keller
Answered 2020-12-03 Author has 90 answers

Rewrite the above differential equation dividing throughout by x as follows
(xy)/x(2x2y)/x=e(x2)/x
=>y2xy=e(x2)/x
y+p(x)y=q(x)withp(x)=2x, q(x)=e(x2)/x
y+p(x)y=q(x)
ye(p(x)dx)=(e(p(x)dx)q(x)dx)+C
Hence, the solution 2xy=e(x2)/x
ye(p(x)dx)=(e(p(x)dx)q(x)dx+C
=>yx(int2xdx)=(e(2xdx))(e(x2)/x)dx+C
=>yx(x2)=(e(x2)(e(x2)/x)dx+C
=>yx(x2)=(1/x)dx+C
=>yx(x2)=ln(x)+C
=>y=(ln(x)+C)/(ex2)
=>y=e(x2)(ln(x)+C)
=>y=e(x2)ln(x)+Ce(x2)
xy2x2y=e(x2) y=e(x2)ln(x)+Ce(x2)

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Jeffrey Jordon
Answered 2021-10-21 Author has 2047 answers

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