Solve the vector differential equation r′(t)=2ti+etj+e−tk with the initial condition r(0)=i−j+k.
Now we use the initial condition r(0)=i−j+k. r(0)=c1i+(1+c2)j+(−1+c3)k=i−j+k from which we find c1=11+c2=−1−1+c3=1c2=−2c3=2
797
The vector function r=r(t) is r(t)=(t2+1)i+(et−2)j+(2−e−t)k