3.44 How to draw isoclines lines for first order ode?

isoclines for first order ode \(y'=f(x,y)\) are the lines \(y=f(x)\) described by solving for \(y\) from equation \(f(x,y)=m\) where \(m\) are the specific slope value.

For different \(m\) values, different equations for \(y\) results, and these are the isoclines. On each such line, the slope is the same.

To plot these in Maple, contourplot is used.

f:=y^2+x-1: #isoclines 
plots:-contourplot(f, x=-10..10, y=-10..10 , 
         legend=true, 
         contours=[0,-1,1,-3,3,-5,5], #specific slope value to show 
         legendstyle=[location=right], 
         size=[500,400], 
         colorscheme="DivergeRainbow", 
         'title'=typeset("isoclines lines for ",diff(y(x),x)=f));