Hello guys, I meet a question when I do the mock quiz 1. First one is finding the solution of y’=(x+y)^2-1? Second one is a solution of y’=x^2/(y+1)? I want to get the whole solution about how to do it, can someone help me?
Dear Yue Yao
thanks for asking this question on the forum.
The first ODE y'=(x+y)^2-1 is of the type y'=f(ax+by+c) with a=1,b=1 and c=0. We have covered this type of ODE in the third lesson of week 1. You can solve it using z=(x+y) and z'=1+y'=(x+y)^2=z^2 leading to z'=z^2. This last equation can be solved by separation of variables. You can then use z=x+y for finding the expression for y.
The second ODE is just a separable first order ODE. You can try to solve it yourself following the method explained in class.
If you have still problems you can ask me in the Q&A tutorial session this week.
thanks for asking this question on the forum.
The first ODE y'=(x+y)^2-1 is of the type y'=f(ax+by+c) with a=1,b=1 and c=0. We have covered this type of ODE in the third lesson of week 1. You can solve it using z=(x+y) and z'=1+y'=(x+y)^2=z^2 leading to z'=z^2. This last equation can be solved by separation of variables. You can then use z=x+y for finding the expression for y.
The second ODE is just a separable first order ODE. You can try to solve it yourself following the method explained in class.
If you have still problems you can ask me in the Q&A tutorial session this week.
