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

Addyson Bright

Answered question

2022-09-17

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

Answer & Explanation

anekesanxl

anekesanxl

Beginner2022-09-18Added 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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