Homework, Section 2.6: pp. 161--, #3, 10, 42
MAT128, Fall, 2015
Andy Long

#3

Clear[x,a,y,fun]
Solve[D[1/x+1/y[x]==1,x],y'[x]]
fun=Solve[1/x+1/y[x]==1,y[x]]
exp=Replace[y[x],fun][[1]]
y[x_]=exp (* use a non-delayed = sign *)
y[3]
Simplify[y'[x]]

#10

Clear[x,y]
Solve[D[y[x]^5+x^2y[x]^3==1+x^4y[x],x],y'[x]]

#42

Clear[x,y]
soln=Solve[D[2y[x]^3+y[x]^2-y[x]^5==x^4-2x^3+x^2,x],y'[x]]
Solve[Replace[y'[x],soln][[1]]==0,x]

solns=Solve[2y^3+y^2-y^5==x^4-2x^3+x^2,x]

exp=Replace[x,solns][[1]]

z1[y_]=Replace[x,solns][[1]]
z2[y_]=Replace[x,solns][[2]]
z3[y_]=Replace[x,solns][[3]]
z4[y_]=Replace[x,solns][[4]]
Plot[{z1[y],z2[y],z3[y],z4[y]},{y,-2,2}]

ContourPlot[
2y^3+y^2-y^5==(x^4-2x^3+x^2),
{x,-2,3},
{y,-2,2}
]