Question

微分方程通解的问题.看图.第一题的答案是3^（-y）+3^x=C

Answer 1

dy/dx=3^x *3^y

3^(-y) dy=3^x dx

-3^(-y)/ln3 = 3^x/ln3 +c1

3^(-y)= 3^x+c

y=-ln(3^x+c)/ln3

dp/p=(1+x^2)/x dx =(1/x +2x)dx

lnp=lnx+x^2 +c

p=c1*x*e^(x^2) c1=±e^c