设f'(t)是连续的已知函数,则方程f'(y/x)(xy'-y)=2(x^3)的通解为_________如题,标答为f(y/x)=x^2+C,麻烦写一下过程~~~谢谢~~~
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![设f'(t)是连续的已知函数,则方程f'(y/x)(xy'-y)=2(x^3)的通解为_________如题,标答为f(y/x)=x^2+C,麻烦写一下过程~~~谢谢~~~](/uploads/image/z/6120599-23-9.jpg?t=%E8%AE%BEf%27%28t%29%E6%98%AF%E8%BF%9E%E7%BB%AD%E7%9A%84%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0%2C%E5%88%99%E6%96%B9%E7%A8%8Bf%27%28y%2Fx%29%28xy%27-y%29%3D2%28x%5E3%29%E7%9A%84%E9%80%9A%E8%A7%A3%E4%B8%BA_________%E5%A6%82%E9%A2%98%2C%E6%A0%87%E7%AD%94%E4%B8%BAf%28y%2Fx%29%3Dx%5E2%2BC%2C%E9%BA%BB%E7%83%A6%E5%86%99%E4%B8%80%E4%B8%8B%E8%BF%87%E7%A8%8B%7E%7E%7E%E8%B0%A2%E8%B0%A2%7E%7E%7E)
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设f'(t)是连续的已知函数,则方程f'(y/x)(xy'-y)=2(x^3)的通解为_________如题,标答为f(y/x)=x^2+C,麻烦写一下过程~~~谢谢~~~
设f'(t)是连续的已知函数,则方程f'(y/x)(xy'-y)=2(x^3)的通解为_________
如题,标答为f(y/x)=x^2+C,麻烦写一下过程~~~谢谢~~~
设f'(t)是连续的已知函数,则方程f'(y/x)(xy'-y)=2(x^3)的通解为_________如题,标答为f(y/x)=x^2+C,麻烦写一下过程~~~谢谢~~~
记u=y/x,则u'=(y'x-y)/x^2
代入有
f'(u)*u'*x^2=2x^3
f'(u)*u'=2x
即[f(u)]'=2x
于是f(u)=x^2+C