(x-2y)y'=2x-y,x^2 -xy+y^2=c,验证所给而原方程所确定的函数为所给微分方程的解
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(x-2y)y''=2x-y,x^2-xy+y^2=c,验证所给而原方程所确定的函数为所给微分方程的解(x-2y)y''=2x-y,x^2-xy+y^2=c,验证所给而原方程所确定的函数为所给微分方程的解
(x-2y)y'=2x-y,x^2 -xy+y^2=c,验证所给而原方程所确定的函数为所给微分方程的解
(x-2y)y'=2x-y,x^2 -xy+y^2=c,验证所给而原方程所确定的函数为所给微分方程的解
(x-2y)y'=2x-y,x^2 -xy+y^2=c,验证所给而原方程所确定的函数为所给微分方程的解
原式为(x-2y)y'=2x-y①
对x∧2-xy+y∧2=c两端关于x隐函数求导,得
2x-y-xy'+2yy'=0
∴xy'-2yy'=2x-y
∴(x-2y)y'=2x-y.②
观察只,①式与②式完全相等,
从而该方程是所给微分方程的解!
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