∵dy/dx=5^(x+y)
==>5^(-y)dy=5^xdx
==>-5^(-y)/ln5=5^x/ln5-C/ln5 (C是积分常数)
==>-5^(-y)=5^x-C
==>5^x+5^(-y)=C
∴原方程的通解是5^x+5^(-y)=C.
dy/dx=5^(x+y)求通解,复制粘贴的不要来了,这道题不太会,求详解.
∵dy/dx=5^(x+y)
==>5^(-y)dy=5^xdx
==>-5^(-y)/ln5=5^x/ln5-C/ln5 (C是积分常数)
==>-5^(-y)=5^x-C
==>5^x+5^(-y)=C
∴原方程的通解是5^x+5^(-y)=C.