CHAPTER 16 - Differential Equations
Section 16.2, page 10 (supplement)
Problem 20
We use the integrating factor as shown:
> | M:=x+2*y; N:=-x; rho:=1/x^3; |
> | diff(rho*M,y)-diff(rho*N,x); |
So the integrating factor works. Now:
> | int(rho*M,x)+c(y); int(rho*N,y)+k(x); |
These agree if c(y) is actually a constant and k(x)=-1/x+ a constant. So the general solution of the equation is
> | %%-c(y)=K; |
for any constant K. Or we could solve this for y and get:
> | y=solve(%,y); |
Section 16.3, page 16 (supplement)
Problem 10
> | simplify(dsolve({x*diff(y(x),x)+2*y(x)=x^3,y(2)=1},y(x))); |
Section 16.4, page 21 (supplement)
Problem 6
> | dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=0,y(x)); |
Problem 18
> | dsolve({4*diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(0)=4,D(y)(0)=2},y(x)); |
Section 16.5, page 34 (supplement)
Problem 14
> | dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=2*x-3,y(x)); |
Problem 43
> | dsolve(diff(y(x),x$2)+2*diff(y(x),x)=x^2-exp(x),y(x)); |
Problem 58
> | dsolve({x*diff(y(x),x$3)-2*diff(y(x),x$2)=0,y(1)=-5,D(y)(1)=2,D(D(y))(1)=3},y(x)); |