y2(x−y)dx=x2(x−y)dy=−z(x2+y2)dx We chooze
P1=z1,Q1=z1,R1=x−y
zy2(x−y)+zx2(x−y)−z(x2+y2)(x−y)=0 Then function u1(x, y, z) is determined as
u1(x,y,z)=∫z1dx+∫z1dy+∫(x−y)dx
zx+zy+(x−y)z=C1
y2(x−y)dx=x2(x−y)dy
y2dx=x2dy
y2dy=x2dx
y3=x3+C2The equations
zx+zy+(x−y)z=C1,y3=x3+C2 constitute the integral curves of the given differential equations.
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Thank you sir/ma'am I only reached upto y3=x3+c Thanks for another solution. Thank you so much.
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