(x^2+y^2)dx-2xydy=0 #HomogeneousDifferentialEquation L478 @MathsPulseChinnaiahKalpana
Maths Pulse - Chinnaiah Kalpana
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(x^2+y^2)dx-2xydy=0 #HomogeneousDifferentialEquation L478 @MathsPulseChinnaiahKalpana
32 998 просмотров · 5 л. назад
Maths Pulse - Chinnaiah Kalpana
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32 998 просмотров · 5 л. назад
@Maths Pulse - Chinnaiah Kalpana
Hello, People!
In this video, we have solved a differential equation which is homogeneous by putting y=vx. Please observe each and every step with patience to learn better.
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Chinnaiah Kalpana🍁
Note:
Homogeneous equation:
A differential equation is said to be a homogeneous equation if it is of the form
dy/dx = f(x,y)/g(x,y)
where, both f(x,y) and g(x,y)are homogeneous functions of x and y of the same degree.
f(x,y) and g(x,y) can be written as
f(x,y)=x^α Φ(y/x) and g(x,y)=x^α Φ(y/x)
given equation becomes,
dy/dx = Φ(y/x)/Ψ(y/x)
put y=vx
then
v+x(dv/dx)=dy/dx
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