10.5.23 problem 30

Internal problem ID [1215]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 30
Date solved : Monday, January 27, 2025 at 04:45:31 AM
CAS classification : [_rational]

\begin{align*} \frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ x^{4}+y^{4}+3 x y+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 60.161 (sec). Leaf size: 1181

DSolve[4*x^3/y[x]^2+3/y[x]+(3*x/y[x]^2+4*y[x])*D[y[x],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*}