Question

用MATLAB求符号函数f=ax3+by2+cx+d分别对x,y进行三次微分；对 y进行定积分和不定积

Answer 1

syms x y a b c d

diff(a*x^3+b*y^2+c*x+d,x,3) % 6*a

diff(a*x^3+b*y^2+c*x+d,y,3) % 0

int(a*x^3+b*y^2+c*x+d,y) % (b*y^3)/3 + (a*x^3 + c*x + d)*y

int(a*x^3+b*y^2+c*x+d,y,0,1) % a*x^3 + c*x + b/3 + d

limit(a*x^3+b*y^2+c*x+d,y,1) % a*x^3 + c*x + b + d

syms y(x) z(x)

s=dsolve(diff(y,x)-z == cos(x),diff(z,x)+y==1,y(0)==1,z(0)==0)

s.z,s.y

% z(x)=-(x*sin(x))/2

% y(x)=sin(x)/2 + (x*cos(x))/2 + 1