Internal problem ID [566]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }=-3 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 326
dsolve(3*x+6/y(x)+(x^2/y(x)+3*y(x)/x)*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-12 x^{3}+\left (-324 x^{2}-108 c_{1} +12 \sqrt {12 x^{9}+729 x^{4}+486 c_{1} x^{2}+81 c_{1}^{2}}\right )^{\frac {2}{3}}}{6 \left (-324 x^{2}-108 c_{1} +12 \sqrt {12 x^{9}+729 x^{4}+486 c_{1} x^{2}+81 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) \left (-324 x^{2}-108 c_{1} +12 \sqrt {12 x^{9}+729 x^{4}+486 c_{1} x^{2}+81 c_{1}^{2}}\right )^{\frac {1}{3}}}{12}-\frac {x^{3} \left (i \sqrt {3}-1\right )}{\left (-324 x^{2}-108 c_{1} +12 \sqrt {12 x^{9}+729 x^{4}+486 c_{1} x^{2}+81 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {12 i \sqrt {3}\, x^{3}+i \sqrt {3}\, \left (-324 x^{2}-108 c_{1} +12 \sqrt {12 x^{9}+729 x^{4}+486 c_{1} x^{2}+81 c_{1}^{2}}\right )^{\frac {2}{3}}+12 x^{3}-\left (-324 x^{2}-108 c_{1} +12 \sqrt {12 x^{9}+729 x^{4}+486 c_{1} x^{2}+81 c_{1}^{2}}\right )^{\frac {2}{3}}}{12 \left (-324 x^{2}-108 c_{1} +12 \sqrt {12 x^{9}+729 x^{4}+486 c_{1} x^{2}+81 c_{1}^{2}}\right )^{\frac {1}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.558 (sec). Leaf size: 331
DSolve[3*x+6/y[x]+(x^2/y[x]+3*y[x]/x)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}{3 \sqrt [3]{2}}-\frac {\sqrt [3]{2} x^3}{\sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}} \\ y(x)\to \frac {\left (-1+i \sqrt {3}\right ) \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}{6 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) x^3}{2^{2/3} \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}} \\ y(x)\to \frac {\left (1-i \sqrt {3}\right ) x^3}{2^{2/3} \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}{6 \sqrt [3]{2}} \\ \end{align*}