(1-x^2)^1/2*y'-(1-y^2)^1/2=0用分离变量法求该方程通解
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(1-x^2)^1/2*y'-(1-y^2)^1/2=0用分离变量法求该方程通解
(1-x^2)^1/2*y'-(1-y^2)^1/2=0用分离变量法求该方程通解
(1-x^2)^1/2*y'-(1-y^2)^1/2=0用分离变量法求该方程通解
∵∫dx/√(1-x²)=arcsinx+C (C是积分常数)
∴由(1-x²)^1/2*y'-(1-y²)^1/2=0
==>dy/√(1-y²)=dx/√(1-x²)
==>arcsiny=arcsinx+C
故 原方程的通解是arcsiny=arcsinx+C (C是积分常数).
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