Multiplied differential equations. How to get x(t),y(t) solutions for "product differential equations" (dotted on t): dot x dot y= xy, dot y^2-dot x^2= 1;

Addyson Bright 2022-09-17 Answered
Multiplied differential equations
How to get x(t),y(t) solutions for "product differential equations" (dotted on t):
x ˙ y ˙ = x y , y ˙ 2 x ˙ 2 = 1 ;
we have by solving quadratics
( 2 y ˙ 2 , 2 x ˙ 2 ) = + 1 ± 1 + 4 x 2 y 2 , 1 ± 1 + 4 x 2 y 2
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Answers (1)

anekesanxl
Answered 2022-09-18 Author has 12 answers
Step 1
You can eliminate y.
x ˙ 2 y ˙ 2 = 1 x ˙ 4 x ˙ 2 y ˙ 2 = x ˙ 2 x ˙ 4 x 2 y 2 = x ˙ 2
Step 2
and
y 2 = x ˙ 4 x ˙ 2 x 2 .

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