Очередная ошибка dsolve

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Markiyan Hirnyk
Сообщения: 1248
Зарегистрирован: Вс дек 04, 2011 11:07 pm

Очередная ошибка dsolve

Сообщение Markiyan Hirnyk » Сб дек 01, 2018 9:19 am

Команда

Код: Выделить всё

sol := dsolve({(diff(y(x), x, x, x))*(diff(y(x), x))^2 = 1, y(1) = 1, (D(y))(1) = 1, ((D@@2)(y))(1) = 1}, y(x));
y(x) = (1/18)*3^(1/2)*(Int(2*3^(1/2)+3*exp(RootOf(3^(1/2)*(-(12*I)*exp(_Z)*Pi*_Z31-6*exp(_Z)*ln(1+(2/3)*3^(1/2))-18*exp(_Z)*3^(1/2)*_z1+3*exp(2*_Z)*3^(1/2)+12*exp(_Z)*3^(1/2)+6*exp(_Z)*_Z-3^(1/2))))+1/exp(RootOf(3^(1/2)*(-(12*I)*exp(_Z)*Pi*_Z31-6*exp(_Z)*ln(1+(2/3)*3^(1/2))-18*exp(_Z)*3^(1/2)*_z1+3*exp(2*_Z)*3^(1/2)+12*exp(_Z)*3^(1/2)+6*exp(_Z)*_Z-3^(1/2)))), _z1 = 1 .. x))+1, y(x) = (1/18)*3^(1/2)*(Int(1/exp(RootOf(3^(1/2)*(-(12*I)*exp(_Z)*Pi*_Z27-6*exp(_Z)*ln(-1+(2/3)*3^(1/2))+18*exp(_Z)*3^(1/2)*_z1+3*exp(2*_Z)*3^(1/2)-12*exp(_Z)*3^(1/2)+6*exp(_Z)*_Z-3^(1/2))))+3*exp(RootOf(3^(1/2)*(-(12*I)*exp(_Z)*Pi*_Z27-6*exp(_Z)*ln(-1+(2/3)*3^(1/2))+18*exp(_Z)*3^(1/2)*_z1+3*exp(2*_Z)*3^(1/2)-12*exp(_Z)*3^(1/2)+6*exp(_Z)*_Z-3^(1/2))))+2*3^(1/2), _z1 = 1 .. x))+1, y(x) = -(1/16)*(1-I*7^(1/2))^(1/2)*(Int(-4*(1-I*7^(1/2))^(1/2)-I*7^(1/2)/exp(RootOf((1-I*7^(1/2))^(1/2)*((4*I)*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*(1-I*7^(1/2))^(3/2)*Pi*_Z31+2*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*ln((1/4)*(1-I*7^(1/2))^(3/2)+1/2+((1/2)*I)*7^(1/2))*(1-I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z+16*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*_z1-I*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)-2*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)-2*exp(_Z)*_Z-3*(1/(1-I*7^(1/2)))^(1/2))))+4*exp(RootOf((1-I*7^(1/2))^(1/2)*((4*I)*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*(1-I*7^(1/2))^(3/2)*Pi*_Z31+2*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*ln((1/4)*(1-I*7^(1/2))^(3/2)+1/2+((1/2)*I)*7^(1/2))*(1-I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z+16*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*_z1-I*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)-2*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)-2*exp(_Z)*_Z-3*(1/(1-I*7^(1/2)))^(1/2))))+1/exp(RootOf((1-I*7^(1/2))^(1/2)*((4*I)*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*(1-I*7^(1/2))^(3/2)*Pi*_Z31+2*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*ln((1/4)*(1-I*7^(1/2))^(3/2)+1/2+((1/2)*I)*7^(1/2))*(1-I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z+16*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*_z1-I*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)-2*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)-2*exp(_Z)*_Z-3*(1/(1-I*7^(1/2)))^(1/2)))), _z1 = 1 .. x))+1, y(x) = -(1/16)*(1+I*7^(1/2))^(1/2)*(Int(-4*(1+I*7^(1/2))^(1/2)+I*7^(1/2)/exp(RootOf((1+I*7^(1/2))^(1/2)*(-(4*I)*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)*Pi*_Z31-2*exp(_Z)*ln((1/4)*(1+I*7^(1/2))^(3/2)+1/2-((1/2)*I)*7^(1/2))*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z-16*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*_z1-I*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+2*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)+2*exp(_Z)*_Z+3*(1/(1+I*7^(1/2)))^(1/2))))+4*exp(RootOf((1+I*7^(1/2))^(1/2)*(-(4*I)*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)*Pi*_Z31-2*exp(_Z)*ln((1/4)*(1+I*7^(1/2))^(3/2)+1/2-((1/2)*I)*7^(1/2))*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z-16*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*_z1-I*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+2*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)+2*exp(_Z)*_Z+3*(1/(1+I*7^(1/2)))^(1/2))))+1/exp(RootOf((1+I*7^(1/2))^(1/2)*(-(4*I)*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)*Pi*_Z31-2*exp(_Z)*ln((1/4)*(1+I*7^(1/2))^(3/2)+1/2-((1/2)*I)*7^(1/2))*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z-16*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*_z1-I*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+2*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)+2*exp(_Z)*_Z+3*(1/(1+I*7^(1/2)))^(1/2)))), _z1 = 1 .. x))+1, y(x) = -(1/16)*(1+I*7^(1/2))^(1/2)*(Int(I*7^(1/2)/exp(RootOf((1+I*7^(1/2))^(1/2)*(-(4*I)*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)*Pi*_Z27-2*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*ln((1/4)*(1+I*7^(1/2))^(3/2)-1/2+((1/2)*I)*7^(1/2))*(1+I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z+16*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*_z1-I*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+2*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)+2*exp(_Z)*_Z+3*(1/(1+I*7^(1/2)))^(1/2))))+1/exp(RootOf((1+I*7^(1/2))^(1/2)*(-(4*I)*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)*Pi*_Z27-2*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*ln((1/4)*(1+I*7^(1/2))^(3/2)-1/2+((1/2)*I)*7^(1/2))*(1+I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z+16*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*_z1-I*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+2*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)+2*exp(_Z)*_Z+3*(1/(1+I*7^(1/2)))^(1/2))))+4*exp(RootOf((1+I*7^(1/2))^(1/2)*(-(4*I)*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*(1+I*7^(1/2))^(3/2)*Pi*_Z27-2*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*ln((1/4)*(1+I*7^(1/2))^(3/2)-1/2+((1/2)*I)*7^(1/2))*(1+I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z+16*exp(_Z)*(1/(1+I*7^(1/2)))^(1/2)*_z1-I*(1/(1+I*7^(1/2)))^(1/2)*7^(1/2)+2*exp(2*_Z)*(1/(1+I*7^(1/2)))^(1/2)+2*exp(_Z)*_Z+3*(1/(1+I*7^(1/2)))^(1/2))))-4*(1+I*7^(1/2))^(1/2), _z1 = 1 .. x))+1, y(x) = (1/16)*(1-I*7^(1/2))^(1/2)*(Int((I*7^(1/2)-4*(exp(RootOf((1-I*7^(1/2))^(1/2)*((4*I)*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*(1-I*7^(1/2))^(3/2)*Pi*_Z27+2*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*ln((1/4)*(1-I*7^(1/2))^(3/2)-1/2-((1/2)*I)*7^(1/2))*(1-I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z-16*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*_z1-I*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)-2*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)-2*exp(_Z)*_Z-3*(1/(1-I*7^(1/2)))^(1/2)))))^2+4*(1-I*7^(1/2))^(1/2)*exp(RootOf((1-I*7^(1/2))^(1/2)*((4*I)*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*(1-I*7^(1/2))^(3/2)*Pi*_Z27+2*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*ln((1/4)*(1-I*7^(1/2))^(3/2)-1/2-((1/2)*I)*7^(1/2))*(1-I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z-16*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*_z1-I*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)-2*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)-2*exp(_Z)*_Z-3*(1/(1-I*7^(1/2)))^(1/2))))-1)/exp(RootOf((1-I*7^(1/2))^(1/2)*((4*I)*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*(1-I*7^(1/2))^(3/2)*Pi*_Z27+2*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*ln((1/4)*(1-I*7^(1/2))^(3/2)-1/2-((1/2)*I)*7^(1/2))*(1-I*7^(1/2))^(3/2)+(2*I)*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)+(2*I)*exp(_Z)*7^(1/2)*_Z-16*exp(_Z)*(1/(1-I*7^(1/2)))^(1/2)*_z1-I*(1/(1-I*7^(1/2)))^(1/2)*7^(1/2)-2*exp(2*_Z)*(1/(1-I*7^(1/2)))^(1/2)-2*exp(_Z)*_Z-3*(1/(1-I*7^(1/2)))^(1/2)))), _z1 = 1 .. x))+1

проиводит 6 решений(!), что не согласуется с

Код: Выделить всё

sol1 := dsolve({(diff(y(x), x, x, x))*(diff(y(x), x))^2 = 1, y(1) = 1, (D(y))(1) = 1, ((D@@2)(y))(1) = 1}, y(x), numeric);
                sol1 := proc(x_rkf45)  ...  end;
plots:-odeplot(sol1, x = 1 .. 2);