Solve the differential equation : dy/dx = (1 + y2)/(1 + x2)

1.	Solve the differential equation : dy/dx = (1 + y2)/(1 + x2)
Answer» Given differential equation is dy/dx = (1 + y²)/(1 + x²) or, (1/(1 + y²)) dy = (1/(1 + x²)) dx on, integrating, ∫(1/(1 + y²)) dx = ∫(1/(1 + x²)) dy or, tan^-1 y = tan^-1 x + c or tan^-1 y - tan^-1 x = c or, tan^-1 ((y - x)/(1 + yx)) = c or, (y - x)/(1 + yx) = tan c ∴ (y - x)/(1 + yx) = c(constant) is, the require solution

Answer»

Given differential equation is dy/dx = (1 + y²)/(1 + x²)

or, (1/(1 + y²)) dy = (1/(1 + x²)) dx

on, integrating,

∫(1/(1 + y²)) dx = ∫(1/(1 + x²)) dy

or, tan^-1 y = tan^-1 x + c

or tan^-1 y - tan^-1 x = c

or, tan^-1 ((y - x)/(1 + yx)) = c

or, (y - x)/(1 + yx) = tan c

∴ (y - x)/(1 + yx) = c(constant) is, the require solution

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