Question

(y²+2x²y)dx+(2x³-xy)dy=0
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Answer 1

Answer:

Step-by-step explanation:

y(y+2x2)dx+x(2x2−y)dy=0

 

Substitute y=tx

t(t+2x)=(t−2x)y′

Note that y′=t′x+t

t(t+2x)=(t−2x)(t′x+t)

After some simplifications you get:

t′(t−2x)=4t

Consider now x′=dxdt

x′+x2t=14