Internal problem ID [13102]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.5 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime }=-6} \]
✓ Solution by Maple
Time used: 0.609 (sec). Leaf size: 59
dsolve(6+12*x^2*y(x)^2+(7*x^3*y(x)+x/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \operatorname {RootOf}\left (x^{10} \textit {\_Z}^{35}-x^{10} \textit {\_Z}^{30}-\frac {1}{c_{1}^{2}}\right )^{15} x^{4} \left (\operatorname {RootOf}\left (x^{10} \textit {\_Z}^{35}-x^{10} \textit {\_Z}^{30}-\frac {1}{c_{1}^{2}}\right )^{5}-1\right ) c_{1} \]
✓ Solution by Mathematica
Time used: 3.003 (sec). Leaf size: 330
DSolve[6+12*x^2*y[x]^2+(7*x^3*y[x]+x/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [-\text {$\#$1}^7-\frac {3 \text {$\#$1}^5}{x^2}-\frac {3 \text {$\#$1}^3}{x^4}-\frac {\text {$\#$1}}{x^6}+\frac {e^{c_1}}{x^{12}}\&,1\right ] y(x)\to \text {Root}\left [-\text {$\#$1}^7-\frac {3 \text {$\#$1}^5}{x^2}-\frac {3 \text {$\#$1}^3}{x^4}-\frac {\text {$\#$1}}{x^6}+\frac {e^{c_1}}{x^{12}}\&,2\right ] y(x)\to \text {Root}\left [-\text {$\#$1}^7-\frac {3 \text {$\#$1}^5}{x^2}-\frac {3 \text {$\#$1}^3}{x^4}-\frac {\text {$\#$1}}{x^6}+\frac {e^{c_1}}{x^{12}}\&,3\right ] y(x)\to \text {Root}\left [-\text {$\#$1}^7-\frac {3 \text {$\#$1}^5}{x^2}-\frac {3 \text {$\#$1}^3}{x^4}-\frac {\text {$\#$1}}{x^6}+\frac {e^{c_1}}{x^{12}}\&,4\right ] y(x)\to \text {Root}\left [-\text {$\#$1}^7-\frac {3 \text {$\#$1}^5}{x^2}-\frac {3 \text {$\#$1}^3}{x^4}-\frac {\text {$\#$1}}{x^6}+\frac {e^{c_1}}{x^{12}}\&,5\right ] y(x)\to \text {Root}\left [-\text {$\#$1}^7-\frac {3 \text {$\#$1}^5}{x^2}-\frac {3 \text {$\#$1}^3}{x^4}-\frac {\text {$\#$1}}{x^6}+\frac {e^{c_1}}{x^{12}}\&,6\right ] y(x)\to \text {Root}\left [-\text {$\#$1}^7-\frac {3 \text {$\#$1}^5}{x^2}-\frac {3 \text {$\#$1}^3}{x^4}-\frac {\text {$\#$1}}{x^6}+\frac {e^{c_1}}{x^{12}}\&,7\right ] \end{align*}