zaddom, Studia, 4 semestr, metody obliczeniowe
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rozw=dsolve('D2y+y=exp(a*t)')rozw =C5*cos(t) + C6*sin(t) + (exp(a*t)*cos(t)*(cos(t) - a*sin(t)))/(a^2 + 1) + (exp(a*t)*sin(t)*(sin(t) + a*cos(t)))/(a^2 + 1)rozw=simple(rozw)rozw =exp(a*t)/(a^2 + 1) + C5*cos(t) + C6*sin(t)rozw=dsolve('D2y+y=exp(a*x)','x')rozw =C8*cos(x) + C9*sin(x) + (exp(a*x)*cos(x)*(cos(x) - a*sin(x)))/(a^2 + 1) + (exp(a*x)*sin(x)*(sin(x) + a*cos(x)))/(a^2 + 1)rozw=simple(rozw)rozw =exp(a*x)/(a^2 + 1) + C8*cos(x) + C9*sin(x)% zadanie 1rozw=Dy+y*tan(t)=(cos(t))^2??? rozw=Dy+y*tan(t)=(cos(t))^2|{Error: The expression to the left of the equals sign is not a valid target for an assignment.}rozw=dsolve('Dy+y*tan(t)=cos(t)^2')rozw =sin(2*t)/2 + C11*cos(t)rozw=simple(rozw)rozw =cos(t)*(C11 + sin(t))rozw=dsolve('D2y+(2/t)*Dy+y=(1/t)')rozw =1/t + (C13*exp(i*t))/t + (C14*i)/(2*t*exp(i*t))rozw=simple(rozw)rozw =(C13*exp(i*t) + (C14*i)/(2*exp(i*t)) + 1)/trozw=dsolve('D2y+2*Dy/t+y=1/t')rozw =1/t + (C13*exp(i*t))/t + (C14*i)/(2*t*exp(i*t))%zadanie 2rozw=dsolve('Dx=y+2*x,Dy=x+sin(t)','x(0)=1/4,y(0)=0')rozw =y: [1x1 sym]x: [1x1 sym]rx=rozw.xrx =sin(t)/(2*(2*2^(1/2) - 4)) - (2*cos(t))/(24*2^(1/2) + 32) - (4*sin(t))/(24*2^(1/2) + 32) - (2^(1/2)*cos(t))/(4*(2*2^(1/2) - 4)) - (2^(1/2)*cos(t))/(24*2^(1/2) + 32) - (2^(1/2)*sin(t))/(4*(2*2^(1/2) - 4)) - (3*2^(1/2)*sin(t))/(24*2^(1/2) + 32) + (6*exp(t)*exp(2^(1/2)*t))/(16*2^(1/2) + 32) - (6*exp(t))/(exp(2^(1/2)*t)*(16*2^(1/2) + 32)) + (6*2^(1/2)*exp(t)*exp(2^(1/2)*t))/(16*2^(1/2) + 32) - (6*2^(1/2)*exp(t))/(exp(2^(1/2)*t)*(16*2^(1/2) + 32))ry=rozw.yry =cos(t)/(2*(2*2^(1/2) - 4)) - (2*sin(t))/(24*2^(1/2) + 32) + (2^(1/2)*cos(t))/(4*(2*2^(1/2) - 4)) - (2^(1/2)*cos(t))/(24*2^(1/2) + 32) - (2^(1/2)*sin(t))/(4*(2*2^(1/2) - 4)) - (2^(1/2)*sin(t))/(24*2^(1/2) + 32) + (6*exp(t)*exp(2^(1/2)*t))/(16*2^(1/2) + 32) + (18*exp(t))/(exp(2^(1/2)*t)*(16*2^(1/2) + 32)) + (12*2^(1/2)*exp(t))/(exp(2^(1/2)*t)*(16*2^(1/2) + 32))rozw=simple(rx)rozw =(((3*2^(1/2))/8 - 1/2)*(exp(2^(1/2)*t)*cos(t)*(3*2^(1/2) + 4) - exp(t)*(3*2^(1/2) + 9/2) + exp(t)*exp(2*2^(1/2)*t)*(3*2^(1/2) + 9/2) - exp(2^(1/2)*t)*sin(t)*(3*2^(1/2) + 4)))/exp(2^(1/2)*t)rozw=simple(ry)rozw =(3*exp(t + 2^(1/2)*t) + 21*exp(t - 2^(1/2)*t) - 24*cos(t) + 8*sin(t) + 3*2^(1/2)*exp(t + 2^(1/2)*t) + 15*2^(1/2)*exp(t - 2^(1/2)*t) - 18*2^(1/2)*cos(t) + 6*2^(1/2)*sin(t))/(8*(3*2^(1/2) + 4))%zadanie 3rozw=dsolve('D2y=2*Dy')rozw =C18 + C19*exp(2*t)y=dsolve('D2y=2*Dy')y =C18 + C19*exp(2*t)%zadanie 4rozw=dsolwe('D2y=(-9)*y'){??? Undefined function or method 'dsolwe' for input arguments of type 'char'.}y=dsolve('D2y/y=-9')y =C21*cos(3*t) + C22*sin(3*t)%zadanie 5y=dsolve('(-k^2)*y=D2y')y =C24*exp(i*k*t) + C25/exp(i*k*t)y=dsolve('D2y=(-k)^2*y')y =C27/exp(k*t) + C28*exp(k*t)y=dsolve('-k^2*D2y=y')y =C30*exp((i*t)/k) + C31/exp((i*t)/k)%zadanie 6fplot('[(exp(-2*x^2+1)+x)/(2*x*sin(x)),-3*x^2+x+8]',[.15,3])x1=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8',15)x1 =1.7555x2=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8'.15)??? x2=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8'.15)|{Error: Unexpected MATLAB expression.}x1=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8'.15)??? x1=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8'.15)|{Error: Unexpected MATLAB expression.}x2=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8',3)x2 =1.7555x1=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8',.15)x1 =0.3931x2=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8',.3)x2 =0.3931x1=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8',.5)x1 =0.3931x2=fzero('-(exp(-2*x^2+1)+x)/(2*x*sin(x))-3*x^2+x+8',1.8)x2 =1.7555pole=quadl('-(exp(-2*x.^2+1)+x)./(2*x.*sin(x))-3*x.^2+x+8',x1,x2)pole =4.9812diary off
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