Course  Materials


1. solve y'+py=q by linode1 and by dsolve.

2. Exact equations the Long method of solution Mdx+Ndy=0.

3. Solve Bernoulli y'+p y =q y^(n).

4. a y''+b y'+c y = 0 ; y=linode20(a,b,c).

5. Reduction of order y''+py'+qy=0. y1 is a solution Find y2=ROO(p,q,y1).

6. a y''+b y'+c y = q1(x); variation is used in y=linode22(a,b,c,q1).

7. ax^2 y''+bxy'+c y = q1(x); Variation is used in y=cauchy_euler(a,b,c,q1).

8. ax^2 y''+aplusb xy'+c y = q1(x); Variation is used in y=aplusb_cauchy_euler(a,aplusb,c,q1).

9. Variation and reduction of order:Find y2 and yp of y''+py'+qy=r. y=varROO(p,q,r,y1).

10. yp=u y1+v y2 . Method of Variation of parameters y''+py'+qy=r. y=variation(p,q,r,y1,y2).

11. 3rd order Method of Variation of parameters y'''+p1y''+p2y'+p3y=r. y=var3(y1,y2,y3,r,x).

12. 4th order Method of Variation of parameters y''''+p1y'''+p2y''+p3y'+p4y=r. y=var4(y1,y2,y3,y4,r,x).

13. Nth order Method of Variation of parameters D^n Y +p1 D^(n-1) y+...+qY=r. y=varvec(y,r,x).

14. Laplace transform of ay''+by'+cy=q1. y(0)=y0,y'(0)=yprime0 y=lapode22(a,b,c,q1,y0,yprime0).

15. Numerical Euler method to print and plot y versus t of y'=f(t,y) with y(a)=ya.R=Euler11{'f',a,b,ya,M)

16. Numerical Euler method to print compare and plot y versus t of y'=f(t,y) with y(a)=ya. R=Euler22{'f',a,b,ya,M)

17. Numerical RK4-Euler-EXACT sample problem plot comparison. y'=f(t,y) with y(a)=ya. R=n2rk4{'f',a,b,ya,M)
18. SYSTEMS+2nd ORDER). RK4-IVP y'=f(t,x,y) x'=g(t,x,y) with y(a)=ya. x(a)=xa R=rk42IVP{'f','g',a,b,xa,ya,M)
19. SYSTEMS+2nd ORDER). RK4-IVP y'=f(t,x,y'') with y(a)=ya. y'(a)=xa R=rks4{f,a,b,Za,M)
20. SYSTEMS+2nd ORDER). BVp rks. for y'=f(t,x,y'') with y(a)=ya. y(b)=yb L=Linsht{f1,f2,a,b,Za,M)
21. sample excercises on cauchy euler.
Copyright ©1998 Beverly J. Volicer and Steven F. Tello, UMass Lowell.  You may freely edit these pages for use in a non-profit, educational setting.  Please include this copyright notice on all pages.