Question

Solve: y dy=(y²-1)(x+1)dx​

Answer 1

Answer:

divide by y^2–1 and multiply by dx to separate as

dy/(y^2–1)=dx/x and use partial fractions to get

dy/(2*(y-1))-dy/(2*(y+1))=dx/x and integrate to obtain

log(y-1)/2-log(y+1)/2=log(x)+k1 and exponentiate to get

sqrt((y-1)/(y+1))=k2*x and square to get (y-1)/(y+1)=k3*x^2 and solve for y as

y=-(k3*x^2+1)/(k3*x^2–1) and this is readily verified

Step-by-step explanation:

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