Internal problem ID [565]
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]
Solve \begin {gather*} \boxed {\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 17
dsolve(4*x^3/y(x)^2+3/y(x)+(3*x/y(x)^2+4*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ x^{4}+y \relax (x )^{4}+3 x y \relax (x )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 80.491 (sec). Leaf size: 1181
DSolve[4*x^3/y[x]^2+3/y[x]+(3*x/y[x]^2+4*y[x])*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {\frac {6 x}{\sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}}-\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}-\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}-\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}} \\ y(x)\to \frac {1}{2} \sqrt {\frac {6 x}{\sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}}-\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}-\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}-\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}} \\ y(x)\to \frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}-\frac {1}{2} \sqrt {-\frac {6 x}{\sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}}-\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}-\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}} \\ y(x)\to \frac {1}{2} \sqrt {-\frac {6 x}{\sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}}-\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}-\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}}+\frac {1}{2} \sqrt {\frac {4 \sqrt [3]{2} \left (x^4-c_1\right )}{\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}+\frac {\sqrt [3]{243 x^2+\sqrt {59049 x^4-6912 \left (x^4-c_1\right ){}^3}}}{3 \sqrt [3]{2}}} \\ \end{align*}