高等数学：习题解答 37 高阶微分方程（117-120页）

高阶微分方程高阶微分方程2013.5.25with(DEtools):de:=diff(y(x),x$2)=x+sin(x)+1;dsolve(de,y(x);with(DEtools):de:=diff(y(x),x$4)=x*exp(x)+2;dsolve(de,y(x);with(DEtools):de:=diff(y(x),x$2)=diff(y(x),x)+x;dsolve(de,y(x);with(DEtools):de:=diff(y(x),x$2)=1+diff(y(x),x)2;dsolve(de,y(x);with(DEtools):de:=y(x)*diff(y(x),x$2)+diff(y(x),x)2=0;dsolve(de,y(x);with(DEtools):de:=y(x)*diff(y(x),x$2)+diff(y(x),x)2=0;dsolve(de,implicit);with(DEtools):de:=diff(y(x),x$2)=diff(y(x),x)2+diff(y(x),x);dsolve(de,y(x);with(DEtools):de:=diff(y(x),x$2)=diff(y(x),x)2+diff(y(x),x);dsolve(de,implicit);with(DEtools):de:=2*y(x)*diff(y(x),x$2)=1+diff(y(x),x)2;dsolve(de,implicit);with(DEtools):de:=2*x*diff(y(x),x)*diff(y(x),x$2)=1+diff(y(x),x)2;dsolve(de,y(x);with(DEtools):de:=diff(y(x),x$2)+diff(y(x),x)2=1;dsolve(de,y(x);dsolve(de,y(0)=0,D(y)(0)=0,y(x);simplify(%);with(DEtools):de:=diff(y(x),x$2)=3*sqrt(y(x);dsolve(de,y(x);dsolve(de,y(0)=1,D(y)(0)=2,y(x);?with(DEtools):p:=-3:q:=2:Q(x):=0:de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):p:=0:q:=a2:Q(x):=0:de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):p:=0:q:=0:Q(x):=0:de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):p:=6:q:=13:Q(x):=0:de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):de:=diff(y(x),x$4)-16*y(x)=0;r:=solve(r4-16=0,r);dsolve(de,y(x);with(DEtools):p:=4:q:=1:Q(x):=0:de:=4*diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(4*r2+p*r+q=0,r);dsolve(de,y(x);dsolve(de,y(0)=2,D(y)(0)=0,y(x);with(DEtools):p:=4:q:=29:Q(x):=0:de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);dsolve(de,y(0)=0,D(y)(0)=15,y(x);with(DEtools):p:=3:q:=2:Q(x):=(x2+1)*exp(2*x):de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):p:=5:q:=6:Q(x):=2*exp(-x):de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):p:=-10:q:=1:Q(x):=(3*x2+x)*exp(x/5):de:=diff(25*y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(25*r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):p:=-2:q:=5:Q(x):=3*x2*exp(x)*(cos(2*x)+sin(2*x):de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);with(DEtools):p:=0:q:=4:Q(x):=-3*sin(3*x):de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);dsolve(de,y(Pi)=1,D(y)(Pi)=1,y(x);with(DEtools):p:=-6:q:=5:Q(x):=4*x+1:de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);dsolve(de,y(0)=1,D(y)(0)=1,y(x);323(21)32xxxyxe或with(DEtools):p:=-6:q:=9:Q(x):=(2*x+1)*exp(3*x):de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);dsolve(de,y(0)=1,D(y)(0)=1,y(x);simplify(%);with(DEtools):p:=0:q:=4:Q(x):=cos(2*x):de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);r:=solve(r2+p*r+q=0,r);dsolve(de,y(x);dsolve(de,y(0)=0,D(y)(0)=0,y(x);