15.8.16 problem 16

Internal problem ID [3019]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 16
Date solved : Monday, January 27, 2025 at 07:08:52 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve((y(x))+(3*x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ x -\frac {y}{2}-\frac {c_{1}}{y^{3}} = 0 \]

✓ Solution by Mathematica

Time used: 60.085 (sec). Leaf size: 1509

DSolve[(y[x])+(3*x-2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}-\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} \\ y(x)\to -\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}+\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} \\ y(x)\to \frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}-\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}+\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} \\ y(x)\to \frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}+\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}+\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} \\ \end{align*}